10th Class Mathematics Circles Question Bank

done Circle Total Questions - 30

• question_answer1)
  In the given figure, 0 is the centre of the circle and AD is a tangent to the circle at A. If \[\angle CAD=55{}^\circ \]and \[\angle ADC=25{}^\circ \], then find \[\angle ABO\].
  A)
   \[10{}^\circ \]  done clear
  B)
   \[20{}^\circ \] done clear
  C)
   \[30{}^\circ \]                          done clear
  D)
   \[40{}^\circ \] done clear
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• question_answer2)
  In the given figure (not to scale), PQ is a tangent segment, drawn to the circle with centre O at P and QR = RO. If \[PQ=3\sqrt{3}\] cm, and ORQ is a line segment, then find the radius of the circle.
  A)
   \[\sqrt{6}\] cm                           done clear
  B)
   \[3\] cm  done clear
  C)
   \[3\sqrt{3}\]cm              done clear
  D)
   \[\frac{5}{3}\]cm done clear
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• question_answer3)
  The length of a tangent from a point A at distance 10 cm from the centre of the circle is 8 cm. Find the radius of the circle.
  A)
   2 cm                            done clear
  B)
   4 cm        done clear
  C)
   6 cm   done clear
  D)
   8 cm done clear
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• question_answer4)
  Two concentric circles are of radii 26 cm and 10 cm. Find the length of the chord of the larger circle which touches the smaller circle.
  A)
   25 cm                          done clear
  B)
   48 cm       done clear
  C)
   56 cm              done clear
  D)
   60 cm done clear
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• question_answer5)
  A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Then
  A)
   \[~AB+CD=AD+BC\] done clear
  B)
   \[AB+AC=BC+BD\] done clear
  C)
   \[AB+BC=CD+DA\] done clear
  D)
   \[AB+BD=BC+CA\] done clear
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• question_answer6)
  In figure, XY and X` Y` are two parallel tangents to a circle with centre 0 and another tangent AB with point of contact C intersecting XY at A and X` Y` at B. then \[\angle AOB\] is                      
  A)
   \[60{}^\circ \]                          done clear
  B)
   \[90{}^\circ \]  done clear
  C)
   \[120{}^\circ \]                        done clear
  D)
   \[150{}^\circ \]  done clear
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• question_answer7)
  In the figure below, PQ & PR are two tangents to circle. Then.
  A)
   \[\theta =120{}^\circ ,\text{ }\alpha =60{}^\circ \]       done clear
  B)
   \[\theta +\alpha =180{}^\circ \] done clear
  C)
   \[\theta =130{}^\circ ,\alpha =50{}^\circ \]      done clear
  D)
   \[\theta +\alpha =210{}^\circ \] done clear
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• question_answer8)
  The parallelogram circumscribing a circle is a
  A)
   Square                         done clear
  B)
   Rectangle done clear
  C)
   Rhombus      done clear
  D)
   Cyclic quadrilateral done clear
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• question_answer9)

  Direction: A \[\Delta \,ABC\] is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure).

  AB is equal to
  A)
   13 cm done clear
  B)
   12 cm                                        done clear
  C)
   11 cm                          done clear
  D)
   14cm                     done clear
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• question_answer10)

  Direction: A \[\Delta \,ABC\] is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure).

  Area of \[\Delta \,ABC\] is
  A)
   \[40\text{ }c{{m}^{2}}\]                     done clear
  B)
   \[64\text{ }c{{m}^{2}}\]        done clear
  C)
   \[81\text{ }c{{m}^{2}}\]                     done clear
  D)
   \[84\text{ }c{{m}^{2}}\] done clear
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• question_answer11)

  Direction: A \[\Delta \,ABC\] is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure).

  AC ? AB equal
  A)
   1 cm                            done clear
  B)
   2 cm         done clear
  C)
   3 cm                            done clear
  D)
   4 cm done clear
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• question_answer12)
  Sum of angles subtended by opposite sides of a quadrilateral at the centre of the circle to which the quadrilateral circumscribes is.
  A)
   \[120{}^\circ \]             done clear
  B)
   \[150{}^\circ \]           done clear
  C)
   \[240{}^\circ \]                        done clear
  D)
   \[180{}^\circ \] done clear
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• question_answer13)
  If radii of two concentric circles are 6 inch and 10 inch, then length of each chord of one circle which is tangent to the other circle is
  A)
   8 inch                           done clear
  B)
   16 inch         done clear
  C)
   20 inch            done clear
  D)
   19 inch done clear
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• question_answer14)
  In figure PQ is a chord of the circle and POR is its diameter such that \[\angle PRQ=50{}^\circ \]. If PT is the tangent to the circle at the point P then \[\angle QPT\]is equal to 
  A)
   \[45{}^\circ \]                          done clear
  B)
   \[60{}^\circ \] done clear
  C)
   \[50{}^\circ \]  done clear
  D)
   \[55{}^\circ \] done clear
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• question_answer15)
                  From a point P which is at a distance of 15 cm from the centre O of a circle of radius 9 cm, the pair of tangents \[P{{T}_{1}}\] and \[P{{T}_{2}}\] to the circle are drawn. Then, the area of the quadrilateral \[P{{T}_{1}}O{{T}_{2}}\] in \[c{{m}^{2}}\] is
  A)
   108                              done clear
  B)
   100            done clear
  C)
   216           done clear
  D)
   66.5 done clear
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• question_answer16)
  Select the incorrect statement:
  A)
   A parallelogram circumscribing a circle is a rhombus. done clear
  B)
   From any point inside the given circle one and only tangent can be drawn to the given circle. done clear
  C)
   The opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. done clear
  D)
   In two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact. done clear
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• question_answer17)
  Find the value of x, in the figure below:
  A)
   6                                 done clear
  B)
   7 done clear
  C)
   9                                 done clear
  D)
   18 done clear
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• question_answer18)
  Look at given figure, a circle touches the side QR of \[\Delta \,PQR\] at S and touches PQ and PR produced at T and U respectively. If PU = 5 inch, then find S where 'S' is half perimeter of \[\Delta \,PQR\]
  A)
   5 inch   done clear
  B)
   3.5 inch done clear
  C)
   13 inch             done clear
  D)
   10.5 inch done clear
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• question_answer19)
  A tangent PT to a circle at A is parallel to a chord BC of the circle. Which of the following is correct statement?
  A)
   PT is the tangent parallel to the chord AB. done clear
  B)
   PT is the tangent parallel to the chord AC. done clear
  C)
   P is equidistant from the extremities of the chord. done clear
  D)
   A is equidistant from the extremities of the chord.   done clear
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• question_answer20)
  LM is a diameter of a circle with centre O. Tangent PT touches the circle at N. If\[\angle MLN=40{}^\circ \], find\[\angle LNP\].
  A)
   \[45{}^\circ \]                          done clear
  B)
   \[80{}^\circ \]           done clear
  C)
   \[50{}^\circ \]         done clear
  D)
   \[140{}^\circ \] done clear
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• question_answer21)
  In the given figure, TP and TQ are tangents to the circle. If \[\angle PAQ=70{}^\circ \], what is \[\angle PTQ\]?
  A)
   \[40{}^\circ \]                          done clear
  B)
   \[30{}^\circ \]           done clear
  C)
   \[35{}^\circ \]       done clear
  D)
   \[45{}^\circ \] done clear
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• question_answer22)
  In the given figure, OP is a radius and PT is a tangent to the circle. If OP = 9 cm and PT = 40 cm, find the distance between T and S
  A)
   28 cm                          done clear
  B)
   38 cm        done clear
  C)
   32 cm   done clear
  D)
   24 cm done clear
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• question_answer23)
  If the distance between two circle of radii R and r is d, find the length of the direct common tangent.
  A)
   \[\sqrt{{{d}^{2}}+{{(R-r)}^{2}}}\]    done clear
  B)
   \[\sqrt{{{d}^{2}}-{{(R+r)}^{2}}}\] done clear
  C)
   \[\sqrt{{{(R+r)}^{2}}+{{d}^{2}}}\]  done clear
  D)
   \[\sqrt{{{d}^{2}}-{{(R-r)}^{2}}}\] done clear
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• question_answer24)

  A tangent PT touches a circle at N. MN is a chord such that \[\angle MNT=63{}^\circ \].

  Find \[\angle MON\], where O is the centre of the circle.
  A)
   \[157.5{}^\circ \]                      done clear
  B)
   \[100{}^\circ \]           done clear
  C)
   \[94.5{}^\circ \]                       done clear
  D)
   \[126{}^\circ \] done clear
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• question_answer25)
  If an equilateral triangle ABC is inscribed in a circle and tangents are drawn at their vertices; then what kind of \[\Delta \] is formed by intersection of tangents?
  A)
   An isosceles \[\Delta \]    done clear
  B)
   A right angled isosceles \[\Delta \] done clear
  C)
   An acute angled \[\Delta \]                  done clear
  D)
   An equilateral \[\Delta \] done clear
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• question_answer26)
  Take vertices of a \[\Delta \,ABC\]as centres and draw three circles with centres A, B, C respectively, each touching the other two externally. If the sides of the triangle are AB = a; BC = b, CA = c, find the radii of three circles in terms of a, b, c.
  A)
   \[a+b+c,\frac{a-b-c}{2},\frac{a+b-c}{2}\] done clear
  B)
   \[\frac{a+b}{2},\frac{b+c}{2},\frac{c+a}{2}\] done clear
  C)
   \[\frac{a}{2},\frac{b}{2},\frac{c}{2}\] done clear
  D)
   \[\frac{a-b+c}{2},\frac{a+b-c}{2},\frac{b+c-a}{2}\] done clear
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• question_answer27)
  P, Q and R are three points on a circle. The tangent at R meets QP produced at T. Given that \[\angle PTR=36{}^\circ \] and \[\angle PRT=48{}^\circ \], find the angle subtended by QP at the centre 'O' of the circle.
  A)
   \[102{}^\circ \]                        done clear
  B)
   \[98{}^\circ \]            done clear
  C)
   \[110{}^\circ \]            done clear
  D)
   \[84{}^\circ \] done clear
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• question_answer28)
  Two circles with centres \[{{C}_{1}}\] and \[{{C}_{2}}\], and radii 9 cm and 6 cm meet each other externally at one point only. Find the length of their common tangent PQ.
  A)
   8 cm                            done clear
  B)
   \[8\sqrt{2}\] done clear
  C)
   \[6\sqrt{6}\] done clear
  D)
   \[2\sqrt{6}\] done clear
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• question_answer29)
  LM is a chord of a circle, the tangent PN at P meets LM produced at N. If PN = 6 units; LM = x units; MN = 4, units, then find 'x'
  A)
   3                                 done clear
  B)
   5         done clear
  C)
   7                                 done clear
  D)
   9 done clear
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• question_answer30)

  Look at the figure, O is the centre of in circle inscribed in\[\Delta \,PQR\].

  Find \[\angle QOR\] if \[\angle QPR=50{}^\circ \]
  A)
   \[95{}^\circ \]                          done clear
  B)
   \[125{}^\circ \]           done clear
  C)
   \[115{}^\circ \]        done clear
  D)
   \[125{}^\circ \] done clear
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