Self Studies

Circles Test - ...

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  • Question 1
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    In the given figure, EC is a tangent to the circle touching it at point B. Find the measure of ACB.

  • Question 2
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    In the given figure with center O, PQ, QR = 16 cm, RS = 18 cm and SP = 14 cm are tangents to the circle with radius 6 cm touching at points J, K, L and M, respectively. If PJ : QJ = 2 : 1, what will be the length of OP?


  • Question 3
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    In the given figure, A and B are centres of the two circles where the area of the bigger circle is 4 times the area of the smaller circle. CD is a common tangent to both the circles at point E, and E is the midpoint of CD. If AC = 10 cm and CE = 8 cm, find the area of DBC.

  • Question 4
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    What will be the measure of ∠BAO in the given figure with O as centre?

  • Question 5
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    What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?

  • Question 6
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    Two intersecting circles of radii cm and 50 cm have a common chord LM. The distance between the centres of the circles is 70 cm. The chord LM intersects the line OX joining the centres of circles in ratio 3 : 4. Find the length of chord LM provided O and X are centre of the respective circles.

  • Question 7
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    DECF is a cyclic quadrilateral where CD is the diameter of the circle and AB is a tangent to the circle. If ∠BCE is 55°, then what will be the value of ∠CDE?


  • Question 8
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    In the following figure, the radius of the circle with centre O is extended to meet a tangent to the circle at a specific point T. Line OT is 3 times the radius of the same circle. What will be the length of the tangent if the radius of the circle is 15 cm?

  • Question 9
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    Three tangents of a circle are joined to make a triangle around the circle. The points where the circle is touching the tangents are P, Q and R; and the vertices where the tangents meet are L, M and N. What will be the value of , if the tangents LM, MN and NL measure 35 cm, 30 cm and 25 cm, respectively?

  • Question 10
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    What will be the measure of ∠QST in the given figure with centre O, if ∠TOQ = 140°?

  • Question 11
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    In the given figure, find the measures of ∠ADB and ∠EOF, if ∠ACH = ∠BCI = 15° and line CO is the angle bisector of ∠ACB. (Point O is the centre of the circle.)

  • Question 12
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    In the given figure, ∠BDC = 60° and ∠BEC measures three-quarters of ∠BOC. Point O and point E are the centres of the smaller and the bigger circle, respectively. Find the measure of ∠BFC.

  • Question 13
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    In the given figure, find the sum of ∠EBD and ∠COD, if ∠EBO = 15°, ∠BAC = 45° and OD is the median of △BOC. Point O is the centre of the given circle.

  • Question 14
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    From the given figure, find the measure of ∠GBI, if ∠DEA = 30° and ∠ACB = 60°. Point O is the centre of the circle.

  • Question 15
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    In the given figure where point O is the centre of both the circles. If ∠LHK = 45° = ∠LIJ, find: ∠CGD + ∠JKO + ∠LIJ - (∠HKP + ∠COD)

  • Question 16
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    In the figure given below, O is the centre of the circle and DE is a tangent to that circle which touches it at point C. Find the measure of ∠BAC.

  • Question 17
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    In the given circle with centre O, XY and PQ are tangents which touch the circle at points A and B respectively. Find the measure of ∠PCY.

  • Question 18
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    In the given circle with centre O, AB and CD are tangents to the circle at points Q and P respectively. Tangents intersect each other at point Z. Find the measure of x.

  • Question 19
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    In the given circle with centre O, AB and AD are tangents to the circle at points B and D respectively and DC = BC. Find the measure of ∠ODC.

  • Question 20
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    In the given figure, O is the centre of the circle and AC and AD are tangents to the circle at points C and D respectively. DB = OC. Find the measure of ∠OCB and ∠COB.

  • Question 21
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    In the given figure, AB and ED are two tangents drawn on two identical circles with centre I and G meeting at one point and ∠DEC and ∠ECD are equal. If ∠FDE = 40°, then find the measure of ∠AEC.

  • Question 22
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    In the given figure with O as centre, diameter of the circle is 6 cm and AB = BC = 8 cm. Find the length of AO.

  • Question 23
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    Column I Column II
    (a) The measure of ∠PTS, of the given circle is
    (i) 80°
    (b) In the given figure, the measure of ∠CAD is



    (ii) 115°
    (c) In the given figure, the measure of angle CBX is


    (iii) 65°

    (a) (b) (c)
    1 (ii) (iii) (i)
    2 (iii) (ii) (i)
    3 (i) (ii) (iii)
    4 (ii) (i) (iii)

  • Question 24
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    In the figure with O as centre, AB, BC and AC are three tangents drawn on a circle with centre O. The length BF = 2 units, length DC = 4 units, AB + AC = 50 units and AB = 26 units. Find the length of the perpendicular drawn from the centre of the circle to BC.

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