9th Class Mathematics Circles Question Bank

done Circles Total Questions - 60

• question_answer1)
  AB is a chord of a circle with centre O and radius 17 cm. If \[OM\bot AB\] and OM = 8 cm, find the length of chord AB.
  A)
   12cm                          done clear
  B)
   30cm done clear
  C)
   15cm              done clear
  D)
     24cm  done clear
  View Solution play_arrow

• question_answer2)
  AB is a chord of length 24 cm of a circle with centre O and radius 13 cm. Find the distance of the chord from the centre.
  A)
   5cm                            done clear
  B)
   6cm        done clear
  C)
  \[\sqrt{407}cm\]          done clear
  D)
     25 cm done clear
  View Solution play_arrow

• question_answer3)
  48 cm long chord of a circle is at a distance of 7 cm from the centre. Find the radius of the circle.
  A)
   5 cm                           done clear
  B)
   17 cm       done clear
  C)
   25 cm             done clear
  D)
     16 cm done clear
  View Solution play_arrow

• question_answer4)
  A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.
  A)
   30 cm             done clear
  B)
   24 cm done clear
  C)
   16 cm             done clear
  D)
     18 cm done clear
  View Solution play_arrow

• question_answer5)
  In the given figure, \[\Delta ABC\] is inscribed in a circle with centre O. If \[\angle ACB={{65}^{o}},\]find\[\angle ABC.\]
  A)
   25°                  done clear
  B)
   35°          done clear
  C)
   90°                  done clear
  D)
     65° done clear
  View Solution play_arrow

• question_answer6)
  An equilateral\[\Delta PQR\]is inscribed in circle with centre O. Find\[\angle QOR.\]
  A)
  \[60{}^\circ \] done clear
  B)
  \[120{}^\circ \]  done clear
  C)
  \[30{}^\circ \]             done clear
  D)
  \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer7)
  In the given figure,\[\Delta XYZ\]is inscribed in a circle with centre O. If the length of the chord YZ is equal to the radius of the circle OY, find the measure of\[\angle XYZ.\]
  A)
  \[60{}^\circ \]                         done clear
  B)
  \[30{}^\circ \]       done clear
  C)
  \[80{}^\circ \]  done clear
  D)
  \[100{}^\circ \] done clear
  View Solution play_arrow

• question_answer8)
  In the given figure, O is the centre of a circle. If \[\angle DAC={{54}^{o}}\]and \[\angle ACB={{63}^{o}},\]find \[\angle DAB.\]
  A)
  \[72{}^\circ \]                           done clear
  B)
  \[54{}^\circ \]        done clear
  C)
  \[81{}^\circ \]        done clear
  D)
  \[27{}^\circ \] done clear
  View Solution play_arrow

• question_answer9)
  Find the value of \[x\] in the following figure.
  A)
  \[45{}^\circ \]                        done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[60{}^\circ \]             done clear
  D)
  \[55{}^\circ \] done clear
  View Solution play_arrow

• question_answer10)
  What is the least number of noncollinear points required to draw a circle passing through them?
  A)
   Two                            done clear
  B)
   Three done clear
  C)
   Four                done clear
  D)
     Nine done clear
  View Solution play_arrow

• question_answer11)
  Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BC are joined. If \[\angle BAD={{30}^{o}}\]and \[\angle CPA={{45}^{o}},\]find \[\angle CBP.\]
  A)
  \[105{}^\circ \]                        done clear
  B)
  \[115{}^\circ \]    done clear
  C)
  \[135{}^\circ \] done clear
  D)
  \[75{}^\circ \] done clear
  View Solution play_arrow

• question_answer12)
  In the given figure,\[\Delta ABC\]is inscribed in a circle. The bisector of\[\angle BAC\]meets BC at D and the circle at E. If EC is joined and \[\angle ECD={{30}^{o}},\]find \[\angle BAC.\]
  A)
  \[30{}^\circ \]                           done clear
  B)
  \[40{}^\circ \]       done clear
  C)
  \[50{}^\circ \]            done clear
  D)
  \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer13)
  In the given figure, POQ is a diameter of a circle with centre O and PQRS is a cyclic quadrilateral.  SQ  is  drawn.  If \[\angle R={{138}^{o}},\]find \[\angle PQS.\]
  A)
  \[90{}^\circ \]                          done clear
  B)
  \[42{}^\circ \] done clear
  C)
  \[48{}^\circ \]               done clear
  D)
  \[38{}^\circ \] done clear
  View Solution play_arrow

• question_answer14)
  The circumference of a circle is 60 cm. An arc subtends 90° at the centre. Find its length.
  A)
   10 cm                         done clear
  B)
   15 cm done clear
  C)
   20 cm             done clear
  D)
     25 cm done clear
  View Solution play_arrow

• question_answer15)
  Two circles intersect in A and E Quadrilaterals PCBA and ABDE ar inscribed in these circles such that PA and CBD are line segments. If \[\angle P\]is \[{{95}^{o}}\] find the value of z.
  A)
  \[65{}^\circ \]   done clear
  B)
  \[105{}^\circ \] done clear
  C)
  \[95{}^\circ \]    done clear
  D)
  \[85{}^\circ \] done clear
  View Solution play_arrow

• question_answer16)
  A circle is divided into 12 equal parts what is the measure of central angle in each arc?
  A)
  \[30{}^\circ \]            done clear
  B)
  \[60{}^\circ \]   done clear
  C)
  \[45{}^\circ \]                     done clear
  D)
  \[48{}^\circ \] done clear
  View Solution play_arrow

• question_answer17)
  In a circle, the major arc is twice the minor arc. What are the corresponding centre angles and the degree measures of the two arcs?
  A)
  \[90{}^\circ \] and \[270{}^\circ \]              done clear
  B)
  \[60{}^\circ \] and \[300{}^\circ \] done clear
  C)
  \[240{}^\circ \] and \[120{}^\circ \] done clear
  D)
  \[140{}^\circ \] and \[220{}^\circ \] done clear
  View Solution play_arrow

• question_answer18)
  In the given figure. ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are drawn. If \[\angle CAD={{40}^{o}}\]and\[\angle BDC={{25}^{o}},\]find \[\angle BCD.\]
  A)
  \[85{}^\circ \]                          done clear
  B)
  \[120{}^\circ \] done clear
  C)
  \[115{}^\circ \] done clear
  D)
  \[95{}^\circ \] done clear
  View Solution play_arrow

• question_answer19)
  A circle with radius 2 units is intersected by a line at points R and T. Find the maximum possible distance between R and T.
  A)
   1 unit              done clear
  B)
  \[2\pi \,\text{units}\]  done clear
  C)
  \[4\pi \,\text{units}\]     done clear
  D)
     4 units done clear
  View Solution play_arrow

• question_answer20)
  O is the centre of the circle as shown in the figure.\[\angle QRP={{35}^{o}}\]and the distance between P and Q through 'O' is 4 cm. What is the measure of\[\angle ROQ?\]
  A)
  \[55{}^\circ \]                        done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[105{}^\circ \]               done clear
  D)
  \[70{}^\circ \] done clear
  View Solution play_arrow

• question_answer21)
  In the figure given, \[\overline{DC}\]is produced to E and if \[\overline{AC}\]is the bisector of\[\angle A,\]find the measure of\[\angle BCD.\]
  A)
  \[120{}^\circ \]                 done clear
  B)
  \[160{}^\circ \]     done clear
  C)
  \[60{}^\circ \]              done clear
  D)
  \[240{}^\circ \] done clear
  View Solution play_arrow

• question_answer22)
  A line AB intersects a circle with centre O and radius 2 cm at a point B. C is any other point on the circle in line with O and A, Find the measure of AC.
  A)
   4 cm                           done clear
  B)
  \[2+\sqrt{2}\,cm\]   done clear
  C)
   \[4\sqrt{2}\,cm\]         done clear
  D)
    \[2+2\sqrt{2}\,cm\] done clear
  View Solution play_arrow

• question_answer23)
  The length of a chord of a circle is equal to the radius of the circle. Determine the angle which this chord subtends on the major segment of the circle.
  A)
  \[30{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer24)
  PQ and XY are two chords of a circle with centre O. If OA = OB, which of the following is correct?
  A)
   PQ > XY                    done clear
  B)
   PQ < XY    done clear
  C)
   PQ || XY      done clear
  D)
     PQ = XY done clear
  View Solution play_arrow

• question_answer25)
  A triangle ABC is inscribed in a circle, the bisectors of whose angles meet the circumference at X, Y and Z. Determine the angles X, Y and Z respectively.
  A)
   \[{{90}^{o}}-\frac{A}{2},{{90}^{o}}-\frac{B}{2},{{90}^{o}}-\frac{C}{2}\] done clear
  B)
   \[{{90}^{o}},{{60}^{o}},{{30}^{o}}\] done clear
  C)
   \[\frac{A}{2},\frac{B}{2},\frac{C}{2}\] done clear
  D)
   \[\frac{B}{2},\frac{A}{2},\frac{A}{2}-\frac{B}{2}\] done clear
  View Solution play_arrow

• question_answer26)
  In the given circle abcd, O is the centre and \[\angle BDC={{42}^{o}}.\]Find the measure of \[\angle ACB.\]
  A)
  \[42{}^\circ \]                        done clear
  B)
  \[45{}^\circ \]     done clear
  C)
  \[48{}^\circ \]  done clear
  D)
  \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer27)
  Two parallel chords on the same side of the centre of a circle are 10 cm and 24 cm long and their distance apart is 7 cm. Determine the radius of the circle.
  A)
   13 cm      done clear
  B)
   8 cm  done clear
  C)
   5 cm               done clear
  D)
     7 cm done clear
  View Solution play_arrow

• question_answer28)
  Into how many parts does a circle divide a plane including itself?
  A)
   2 parts                        done clear
  B)
   3 parts done clear
  C)
   4 parts            done clear
  D)
     5 parts done clear
  View Solution play_arrow

• question_answer29)
  Given two concentric circles with centre O. A line cuts the circles at A, B, C and D respectively. Lf AB=10 cm, find the length of CD.
  A)
   5 cm                           done clear
  B)
   10 cm done clear
  C)
   7.5 cm            done clear
  D)
     15 cm done clear
  View Solution play_arrow

• question_answer30)
  A chord of a circle divides the circular region into two parts. What is the region that contains the centre?
  A)
   Minor Arc                   done clear
  B)
   Major Arc    done clear
  C)
   Minor Segment           done clear
  D)
   Major Segment done clear
  View Solution play_arrow

• question_answer31)
  In the given figure, find the value of y.
  A)
  \[35{}^\circ \]                        done clear
  B)
  \[{{60}^{o}}+{{x}^{o}}\]      done clear
  C)
  \[{{60}^{o}}-{{x}^{o}}\]             done clear
  D)
  \[120{}^\circ \] done clear
  View Solution play_arrow

• question_answer32)
  An equilateral\[\Delta ABC\] is inscribed in a circle with centre O. Find the measure of \[\angle BOC.\]
  A)
  \[110{}^\circ \] done clear
  B)
  \[100{}^\circ \] done clear
  C)
  \[120{}^\circ \] done clear
  D)
  \[130{}^\circ \] done clear
  View Solution play_arrow

• question_answer33)
  In the given figure, ABDC is a cyclic quadrilateral and AB = AC. If \[\angle ACB={{70}^{o}},\]find \[\angle BDC.\]
  A)
  \[100{}^\circ \] done clear
  B)
  \[70{}^\circ \] done clear
  C)
  \[140{}^\circ \] done clear
  D)
  \[40{}^\circ \] done clear
  View Solution play_arrow

• question_answer34)
  When are two circles said to be concentric?
  A)
   If they have the same radius. done clear
  B)
   If they have different radii. done clear
  C)
   If they have the same centre. done clear
  D)
   If their centres are collinear. done clear
  View Solution play_arrow

• question_answer35)
  In the given figure,\[\overset\frown{PQR}=\overset\frown{SRQ.}\] Which of the following is correct?
  A)
  \[PQ\ne SR\]                done clear
  B)
  \[PS=QR\]    done clear
  C)
  \[PQ=SR\]      done clear
  D)
    \[PS\ne QR\] done clear
  View Solution play_arrow

• question_answer36)
  'O' is the centre of a circle,\[\angle BOA={{90}^{o}}\] and \[\angle COA={{110}^{o}}.\]Find the measure of \[\angle BAC.\]
  A)
  \[70{}^\circ \] done clear
  B)
  \[80{}^\circ \] done clear
  C)
  \[120{}^\circ \] done clear
  D)
  \[50{}^\circ \] done clear
  View Solution play_arrow

• question_answer37)
  In the given figure, O is the centre of the circle, \[OM\bot BC,OL\bot AB,ON\bot AC\]and\[OM=ON=OL.\]What is\[\Delta ABC?\]
  A)
   Right angled triangle done clear
  B)
   Scalene triangle done clear
  C)
   Isosceles triangle done clear
  D)
   Equilateral triangle done clear
  View Solution play_arrow

• question_answer38)
  In the given figure, O is the centre of a circle having radius 5 cm. If \[OM\bot PQ\]and OM = 3 cm, find the length of chord PQ.
  A)
   5 cm                           done clear
  B)
   8 cm  done clear
  C)
   10 cm             done clear
  D)
     6 cm done clear
  View Solution play_arrow

• question_answer39)
  In the given figure, O is the centre of the circle and\[OM\bot PQ.\] If PQ = 6 cm and OM = 4 cm, find the radius of the circle.
  A)
   6cm                            done clear
  B)
   3cm        done clear
  C)
   2 cm               done clear
  D)
     5 cm done clear
  View Solution play_arrow

• question_answer40)
  In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If \[\angle PRQ=l\]and\[\angle OPQ=m,\]what is the value of\[l+m?\]
  A)
   Greater than \[90{}^\circ \] done clear
  B)
   Less than \[90{}^\circ \] done clear
  C)
   Equal to \[180{}^\circ \] done clear
  D)
   Equal to \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer41)
  In the given figure, O is the centre of the circle. If \[\angle POQ={{110}^{o}}\]and\[\angle POR={{120}^{o}},\] find\[\angle QPR.\]
  A)
  \[65{}^\circ \]                             done clear
  B)
  \[55{}^\circ \]  done clear
  C)
  \[50{}^\circ \]        done clear
  D)
  \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer42)
  If O is the centre of the given circle with \[\angle ACB={{60}^{o}},\]find the value of \[x.\]
  A)
  \[120{}^\circ \]                         done clear
  B)
  \[100{}^\circ \]      done clear
  C)
  \[240{}^\circ \]               done clear
  D)
  \[180{}^\circ \] done clear
  View Solution play_arrow

• question_answer43)
  AD is a diameter of a circle and AB is a chord. If AD = 34 cm and AB = 30 cm, find the distance of AB from the centre of the circle.
  A)
   17 cm                         done clear
  B)
   15 cm done clear
  C)
   4 cm               done clear
  D)
     8 cm done clear
  View Solution play_arrow

• question_answer44)
  In the given figure, O is the centre of the circle of radius 5 cm. AB and AC are two chords, such that AB = AC = 6 cm. If OA meets BC at M, find OM,
  A)
   2 cm                           done clear
  B)
   3 cm  done clear
  C)
   1.4 cm                        done clear
  D)
   3.6 cm done clear
  View Solution play_arrow

• question_answer45)
  The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8 cm and RB = 4 cm. find the radius of the circle.
  A)
   10 cm                         done clear
  B)
   8 cm  done clear
  C)
   16 cm             done clear
  D)
     6 cm done clear
  View Solution play_arrow

• question_answer46)
  In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of \[\angle BAC-\angle OBC\]
  A)
  \[90{}^\circ \] done clear
  B)
  \[120{}^\circ \]       done clear
  C)
  \[60{}^\circ \]           done clear
  D)
  \[45{}^\circ \] done clear
  View Solution play_arrow

• question_answer47)
  In the given figure, O is the centre of the circle. The angle subtended by the arc BCD at the centre is 140°. If BC is produced to P, find \[\angle DCP.\]
  A)
  \[60{}^\circ \]        done clear
  B)
  \[110{}^\circ \] done clear
  C)
  \[70{}^\circ \]      done clear
  D)
  \[80{}^\circ \] done clear
  View Solution play_arrow

• question_answer48)
  In the given figure, ABCD and ABPD are cyclic quadrilaterals. If\[\angle BOD={{160}^{o}},\]find the difference of \[\angle BPD\]and \[\angle BCD.\]
  A)
  \[80{}^\circ \]                        done clear
  B)
  \[90{}^\circ \]      done clear
  C)
  \[0{}^\circ \]            done clear
  D)
  \[110{}^\circ \] done clear
  View Solution play_arrow

• question_answer49)
  In the given figure, O is the centre of the circle. If \[\angle ABC={{110}^{o}},\]find\[x.\]
  A)
  \[70{}^\circ \]      done clear
  B)
  \[140{}^\circ \] done clear
  C)
  \[60{}^\circ \]        done clear
  D)
  \[120{}^\circ \] done clear
  View Solution play_arrow

• question_answer50)
  In the given figure, \[\Delta ABC\]is an isosceles triangle with AB = AC and\[\angle ABC={{50}^{o}}.\]Find the sum of \[\angle BDC\]and\[\angle BEC.\]
  A)
  \[30{}^\circ \]          done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[50{}^\circ \]           done clear
  D)
  \[180{}^\circ \]     done clear
  View Solution play_arrow

• question_answer51)
  If the radius of a circle is 10 cm, find the length of a chord of the circle which is at a distance of 6 cm from its centre.
  A)
   16 cm                         done clear
  B)
   10 cm done clear
  C)
   12 cm             done clear
  D)
     14 cm done clear
  View Solution play_arrow

• question_answer52)
  Given a chord AB in a circle as shown. If two more chords AD and BE are drawn perpendicular to AB which of the following is correct?
  A)
   AD = BE                    done clear
  B)
   AD = 2BE   done clear
  C)
   2AD = BE     done clear
  D)
     AD = 3BE done clear
  View Solution play_arrow

• question_answer53)
  In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm. What is the distance of the centre of the circle from BC?
  A)
   1.4 cm                        done clear
  B)
   2.1 cm done clear
  C)
   2.4 cm            done clear
  D)
     2.7 cm done clear
  View Solution play_arrow

• question_answer54)
  Angles subtended by chords AC and BC at the centre O of the circle are 55° and 155° respectively. What is the measure of\[\angle ACB?\]
  A)
  \[65{}^\circ \] done clear
  B)
  \[75{}^\circ \]  done clear
  C)
  \[105{}^\circ \]                done clear
  D)
  \[135{}^\circ \] done clear
  View Solution play_arrow

• question_answer55)
  ABCD is a cyclic quadrilateral in which\[\angle DBC={{55}^{o}}\] and \[\angle BAC={{55}^{o}}.\]Find \[\angle BCD.\]
  A)
  \[60{}^\circ \]                            done clear
  B)
  \[80{}^\circ \]       done clear
  C)
  \[100{}^\circ \]            done clear
  D)
  \[120{}^\circ \] done clear
  View Solution play_arrow

• question_answer56)
  BC is a chord of a circle with centre O. A is a point on major arc BC. Find the total measure of \[\angle BAC\]and \[\angle OBC\]
  A)
  \[90{}^\circ \]                             done clear
  B)
  \[100{}^\circ \] done clear
  C)
  \[120{}^\circ \] done clear
  D)
  \[150{}^\circ \] done clear
  View Solution play_arrow

• question_answer57)
  AB is a chord of a circle of radius 4.3 en and P is a point on AB which divides I into two parts in the ratio 7:10. If P is 2.7 cm away from the centre O, find the length of AB.
  A)
   5 cm               done clear
  B)
     6.8 cm done clear
  C)
   6.4 cm            done clear
  D)
     6.1 cm done clear
  View Solution play_arrow

• question_answer58)
  The radius of a circle is 2.5 cm. AB and CF are two parallel chords 2.7 cm apart. If AB = 4.8 cm, find the measure of CD.
  A)
   4.8 cm                        done clear
  B)
   2.4 cm done clear
  C)
   3 cm               done clear
  D)
     4 cm done clear
  View Solution play_arrow

• question_answer59)
  A quadrilateral ABCD is inscribed in c circle as shown. If \[\angle B={{125}^{o}}\]and E is a point on the circle find \[\angle AEC.\]
  A)
  \[55{}^\circ \]                     done clear
  B)
  \[125{}^\circ \] done clear
  C)
  \[130{}^\circ \]           done clear
  D)
  \[62.5{}^\circ \] done clear
  View Solution play_arrow

• question_answer60)
  ABCD is a quadrilateral whose vertices arc on a semicircle such that AB = BC = CD = 10 cm and AD is diameter of the circle with centre O. Find the perimeter of the
  A)
   80 cm                         done clear
  B)
   70 cm done clear
  C)
   60 cm done clear
  D)
                 50 cm done clear
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