10th Class Mathematics Circles Question Bank

done Circles Total Questions - 25

• question_answer1)
  In the given figure, PT touches the circle at R whose centre is O. Diameter SQ when produced meets PT at P. Given \[\angle SPR={{x}^{o}}\]and \[\angle QRP={{y}^{o}}\]. Then,
  A)
  \[{{x}^{o}}+2{{y}^{o}}={{90}^{o}}\]          done clear
  B)
  \[2{{x}^{o}}+{{y}^{o}}={{90}^{o}}\] done clear
  C)
           \[{{x}^{o}}+{{y}^{o}}={{120}^{o}}\] done clear
  D)
         \[3{{x}^{o}}+2{{y}^{o}}={{120}^{o}}\] done clear
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• question_answer2)
  In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are \[AB=6\text{ }cm,\text{ }BC=7\text{ }cm,\]\[CD=4\text{ }cm,\]then AD equals _____.  
  A)
  10 cm              done clear
  B)
         13 cm              done clear
  C)
         11 cm              done clear
  D)
         3 cm                                        done clear
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• question_answer3)
  In the given figure, a circle touches the side SC of \[\Delta ABC\]at P and touches AB and /AC produced at Q and R respectively. If \[AQ=5\,cm,\] find the perimeter of \[\Delta ABC\].                                 
  A)
  11 cm              done clear
  B)
         10 cm                          done clear
  C)
         6 cm                            done clear
  D)
         7 cm                done clear
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• question_answer4)
  In the given figure, AB and PQ intersect at M. If A and B are centres of circles then ____.
  A)
  \[PM=MQ\]                 done clear
  B)
         \[PQ\bot AB\]              done clear
  C)
         Both (A) and (B)          done clear
  D)
         \[PQ=AB\]          done clear
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• question_answer5)
  BC is the diameter of a semicircle. The sides AB and AC of a triangle ABC meet the semicircle at P and Q respectively. PQ subtends \[{{140}^{o}}\]at the centre of the semicircle. Then \[\angle A\] is _____.
  A)
  \[{{10}^{o}}\]              done clear
  B)
                     \[{{20}^{\text{o}}}\]           done clear
  C)
         \[{{30}^{o}}\]             done clear
  D)
         \[{{40}^{o}}\] done clear
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• question_answer6)
  Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is _____.
  A)
  \[\sqrt{7}\,cm\]            done clear
  B)
         \[3\sqrt{7}\,cm\]                      done clear
  C)
         \[4\sqrt{7}\,cm\]          done clear
  D)
         \[(8+2\sqrt{7})\,cm\] done clear
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• question_answer7)
  In the given figure, ABCD is a cyclic quadrilateral and PQ is tangent to the circle with centre '0'. BD is diameter. \[\angle DCO={{40}^{o}},\] \[\angle ABD={{60}^{o}}\]. Then \[\angle BCP=\] _____.
  A)
  \[{{50}^{o}}\]                done clear
  B)
         \[{{100}^{o}}\]                    done clear
  C)
         \[{{60}^{o}}\]                      done clear
  D)
         \[{{20}^{o}}\]                      done clear
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• question_answer8)
  In the following figure, PT is of length 8 cm. OP is 10 cm. Then the radius of the circle is _____.         
  A)
  2 cm                done clear
  B)
         18 cm              done clear
  C)
                     (5/4) cm                       done clear
  D)
         6 cm                done clear
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• question_answer9)
  A circle inscribed in \[\Delta \,ABC\] having \[AB=10\text{ }cm,\]\[BC=12\text{ }cm,\text{ }CA=28\text{ }cm\]touching sides at D, E, F (respectively). Then \[AD+BE+CF\]is _____.
  A)
  25 cm                          done clear
  B)
         20 cm                          done clear
  C)
         22 cm                          done clear
  D)
         18 cm              done clear
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• question_answer10)
  In the given figure, O is the centre of the circle, then \[\angle XOZ\] is _____.
  A)
  \[2\angle XZY\]             done clear
  B)
         \[2\angle Y\]              done clear
  C)
         \[2\angle Z\] done clear
  D)
         \[2(\angle XZY+\angle YXZ)\] done clear
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• question_answer11)
  In the given figure, O is the centre and SAT is a tangent to the circle at A. If\[\angle BAT=30{}^\circ ,\] find \[\angle AOB\] and \[\angle AQB\].                        
  A)
  \[{{60}^{o}},{{150}^{o}}\]                     done clear
  B)
         \[{{30}^{o}},{{150}^{o}}\]                     done clear
  C)
         \[{{60}^{o}},{{60}^{o}}\]           done clear
  D)
         None of these     done clear
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• question_answer12)
  In the given figure, O is the centre of the circle. Determine \[\angle ABC\] and Reflex\[\angle AOC\]
  A)
  \[{{68}^{o}}.\text{ }{{136}^{o}}\]               done clear
  B)
         \[{{68}^{o}}.\text{ }{{68}^{o}}\]                        done clear
  C)
         \[{{68}^{o}}.\text{ 22}{{\text{4}}^{o}}\]                       done clear
  D)
         \[{{34}^{o}}.\text{ 13}{{\text{6}}^{o}}\]                       done clear
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• question_answer13)
  In the given figure, O is the centre of the circle. If PA and PB are tangents, then the value of \[\angle AQB\] is               
  A)
  \[{{100}^{o}}\]                    done clear
  B)
         \[{{80}^{o}}\]                      done clear
  C)
         \[{{60}^{o}}\]                      done clear
  D)
         \[{{50}^{o}}\]                      done clear
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• question_answer14)
  Two concentric circles of radii a and b, where \[a>b,\]are given. The length of a chord of the larger circle which touches the other circle is                      
  A)
  \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]                done clear
  B)
         \[2\sqrt{{{a}^{2}}-{{b}^{2}}}\]              done clear
  C)
         \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]              done clear
  D)
         \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] done clear
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• question_answer15)
  In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP == 12 cm, find the length of BP.
  A)
  12 cm              done clear
  B)
         \[12.65\text{ }cm\]                  done clear
  C)
         \[12.36\,cm\]                done clear
  D)
         \[12.56\,cm\]                done clear
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• question_answer16)
  Let s denote the semi perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, find BD.
  A)
  \[s-b\]               done clear
  B)
         \[2s+h\]                       done clear
  C)
         \[b+s\]             done clear
  D)
         \[3b-s\] done clear
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• question_answer17)
  In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. lf \[\angle PBT={{30}^{o}},\] then \[BA:AT\]is                        
  A)
  \[3:1\]              done clear
  B)
         \[4:1\]                        done clear
  C)
                                 \[2:1\]                           done clear
  D)
         \[3:2\] done clear
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• question_answer18)
  A circle with centre O touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Find\[\angle AOD+\angle BOC.\].
  A)
  \[{{90}^{o}}\]                      done clear
  B)
         \[{{180}^{o}}\]                    done clear
  C)
         \[{{160}^{o}}\]                    done clear
  D)
         \[{{100}^{o}}\]                    done clear
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• question_answer19)
  How many tangents can a circle have?
  A)
  1                                  done clear
  B)
         2                      done clear
  C)
         4                                  done clear
  D)
         Infinite             done clear
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• question_answer20)
  If O is the centre of a circle, AOC is its diameter and B is a point an the circle such that\[\angle ACB={{50}^{o}}\]. If AT is the tangent to the circle at the point A, then \[\angle BAT=\]
  A)
  \[{{40}^{o}}\]                      done clear
  B)
         \[{{50}^{o}}\]                                  done clear
  C)
         \[{{60}^{o}}\]                      done clear
  D)
         \[{{65}^{o}}\]         done clear
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• question_answer21)
  In the given figure, A and B are the centres of two circles that intersect at X and V. PXQ is a straight line. If reflex angle \[QBY={{210}^{o}},\]find obtuse angle PAY.    
  A)
  \[{{210}^{o}}\]                    done clear
  B)
         \[{{150}^{o}}\] done clear
  C)
         \[{{160}^{o}}\]                                done clear
  D)
         \[{{120}^{o}}\]                                done clear
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• question_answer22)
  AB is a chord of length 24 cm of a circle of radius 13 cm. The tangents at A and B intersect at a point C. Find the length AC.
  A)
  \[31.2\,cm\]                  done clear
  B)
         \[12\,cm\]                     done clear
  C)
         \[28.8\text{ }cm\]        done clear
  D)
         \[25\text{ }cm\]           done clear
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• question_answer23)
  Match the columns.

  Column-l	Column-ll
  (a) Radius of the given  circle is	(p) 20 cm
  (b) In the given figure, value of x is	(q) 6 cm
  (c) Perimeter of APST with  \[PQ=10\text{ }cm\]is	(r) 5 cm

   
  A)
                 (a) \[\to \] (p), (b) \[\to \] (r), (c) \[\to \] (q) done clear
  B)
         (a) \[\to \] (r), (b) \[\to \] (q), (c) \[\to \] (p) done clear
  C)
         (a) \[\to \] (q), (b) \[\to \] (r), (c) \[\to \] (p) done clear
  D)
         (a) \[\to \] (r), (b) \[\to \] (p), (c) \[\to \] (q) done clear
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• question_answer24)
  The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD.
  A)
  19 cm                          done clear
  B)
         20 cm              done clear
  C)
         16 cm                          done clear
  D)
         \[\sqrt{150}\,cm\] done clear
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• question_answer25)
  In the given figure, O is the centre of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that \[\angle SQL={{50}^{o}}\]and \[\angle SRM={{60}^{o}}\]. Then, find \[\angle QSR\] and \[\angle RPQ\].
  A)
  \[{{40}^{o}},{{140}^{o}}\]                     done clear
  B)
         \[{{50}^{o}},{{140}^{o}}\]                     done clear
  C)
                     \[{{60}^{o}},{{120}^{o}}\]                     done clear
  D)
         \[{{70}^{o}},\text{ }{{40}^{o}}\]     done clear
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