SSC Quantitative Aptitude Circular Measurement Question Bank

done Circle and Its Properties (II) Total Questions - 20

• question_answer1)
  PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ will be [SSC CGL Tier II, 2017]
  A)
  3 cm done clear
  B)
  4 cm done clear
  C)
  5 cm done clear
  D)
  2 cm done clear
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• question_answer2)
  Two equal circles intersect so that their centres and the points at which they intersect form a square of side 1 cm. The area of the portion that is common to the circles is [SSC CGL Tier II, 2017]
  A)
  \[\frac{\pi }{4}\,sq\,cm\] done clear
  B)
  \[\frac{\pi }{2}-1\,sq\,cm\] done clear
  C)
  \[\frac{\pi }{5}sq\,cm\] done clear
  D)
  \[(\sqrt{2}-1)\ sq\ cm\] done clear
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• question_answer3)
  A and B are centres of two circles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circle. If AB = 13 cm, then length of PQ Will be  [SSC CGL Tier II, 2015]
  A)
  13 cm done clear
  B)
  8.5 cm done clear
  C)
  12 cm done clear
  D)
  17 cm done clear
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• question_answer4)
  AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm, respectively. If the chords are on the same side of the centre and the  distance between them is 3 cm, then the diameter of the circle is [SSC CGL Tier II, 2015]
  A)
  \[\sqrt{29}\,cm\] done clear
  B)
  \[2\sqrt{21}\,cm\] done clear
  C)
  \[\sqrt{21}\,cm\] done clear
  D)
  \[2\sqrt{29}\,cm\] done clear
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• question_answer5)
  ABCD is a cyclic quadrilateral. AB and DC when produced meet at P, if PA = 8 cm, PB = 6 cm, PC = 4 cm, then the length (in cm) of PD is [SSC CGL Tier II, 2015]
  A)
  6 done clear
  B)
  10 done clear
  C)
  12 done clear
  D)
  8 done clear
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• question_answer6)
  Let C be a point on a straight line AB. Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets the other circle at Q, then
  A)
  \[OC\parallel PB\] done clear
  B)
  OC is never parallel of PB done clear
  C)
  \[QC=\frac{1}{2}PB\] done clear
  D)
  \[QC\parallel PB\] and \[QC=\frac{1}{2}PB\] done clear
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• question_answer7)
  If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is
  A)
  6 cm done clear
  B)
  7 cm done clear
  C)
  10 cm done clear
  D)
  8 cm done clear
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• question_answer8)
  Two chords of a circle, of lengths 2a and 2b are mutually perpendicular. If the distance of the point, at which the chords intersect, from the centre of the circle is c (c radius of the circle), then the radius of the circle is
  A)
  \[a+b+c\] done clear
  B)
  \[\frac{\sqrt{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}}{2}\] done clear
  C)
  \[\frac{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}}{2}\] done clear
  D)
  \[\frac{\sqrt{ab}}{c}\] done clear
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• question_answer9)
  Two concentric circles having common centre 'O' and chord AB of the outer circle intersect the inner circle at points C and D. If distance of chord from the centre is 3 cm, outer radius is 13 cm and inner  radius is 7 cm, then length of AC (in cm) is
  A)
  \[8\sqrt{10}\] done clear
  B)
  \[6\sqrt{10}\] done clear
  C)
  \[4\sqrt{10}\] done clear
  D)
  \[2\sqrt{10}\] done clear
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• question_answer10)
  If PT is a tangent and AB is a chord of a circle and they intersect at the point P externally and PT= 2 AP and AB = 18 units, then PT equals to
  A)
  6 units done clear
  B)
  9 units done clear
  C)
  12 units done clear
  D)
  15 units done clear
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• question_answer11)
  AB is the diameter of a circle with centre O and P is a point on it. If \[\angle POA=120{}^\circ ,\]then the value of \[\angle PBO\]is
  A)
  \[30{}^\circ \] done clear
  B)
  \[50{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[40{}^\circ \] done clear
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• question_answer12)
  A, B, C are three points on a circle. The tangent at A meets BC produced at T, \[\angle BTA=40{}^\circ ,\]\[\angle CAT=44{}^\circ .\]The angle subtended by BC at the centre of the circle is
  A)
  \[84{}^\circ \] done clear
  B)
  \[92{}^\circ \] done clear
  C)
  \[96{}^\circ \] done clear
  D)
  \[104{}^\circ \] done clear
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• question_answer13)
  If the length of a chord of a circle at a distance of 12 cm from the centre is 10 cm, then the diameter of the circle is
  A)
  13 cm done clear
  B)
  15 cm done clear
  C)
  26 cm done clear
  D)
  30 cm done clear
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• question_answer14)
  A is the centre of circle whose radius is 8 and B is the centre of a circle whose diameter is 8. If these two circles touch externally, then the area of the circle with diameter AB is
  A)
  \[36\,\pi \] done clear
  B)
  \[64\,\pi \] done clear
  C)
  \[144\,\pi \] done clear
  D)
  \[256\,\pi \] done clear
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• question_answer15)
  Two chords of lengths a m and b m subtend angles \[60{}^\circ \]and \[90{}^\circ \]at the centre of the circle respectively. Which of the following is true?
  A)
  \[b=\sqrt{2}a\] done clear
  B)
  \[a=\sqrt{2}b\] done clear
  C)
  \[a=2b\] done clear
  D)
  \[b=2a\] done clear
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• question_answer16)
  Two chords AB and CD of a circle with centre O, intersect each other at P. If \[\angle AOD=100{}^\circ \]and \[\angle BOC=70{}^\circ ,\] then the value of \[\angle APC\] is
  A)
  \[80{}^\circ \] done clear
  B)
  \[75{}^\circ \] done clear
  C)
  \[85{}^\circ \] done clear
  D)
  \[95{}^\circ \] done clear
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• question_answer17)
  If 0 is the centre of the circle and PA and PB are tangents, what is the value of\[\angle APB\]?
  A)
  \[40{}^\circ \] done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[80{}^\circ \] done clear
  D)
  \[100{}^\circ \] done clear
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• question_answer18)
  In the figure shown, O is the centre of the circle, \[\angle AOB=25{}^\circ \]and \[\angle BOC\]then \[\angle BOC\]is equal to
  A)
  \[85{}^\circ \] done clear
  B)
  \[150{}^\circ \] done clear
  C)
  \[110{}^\circ \] done clear
  D)
  \[27\frac{1{}^\circ }{2}\] done clear
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• question_answer19)
  In a circle of radius 4 cm with centre at O, AB and CD are two diameters perpendicular to each other. The length of chord BD is
  A)
  \[4\,cm\] done clear
  B)
  \[4\sqrt{2}\,cm\] done clear
  C)
  \[4\sqrt{3}\] done clear
  D)
  None of these done clear
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• question_answer20)
    If TA is a tangent to the circle at B, what is the value of x + y + z?
  A)
  \[56{}^\circ \] done clear
  B)
  \[112{}^\circ \] done clear
  C)
  \[28{}^\circ \] done clear
  D)
  \[65{}^\circ \] done clear
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