# Class 10 – Circles – Previous Years Questions

Previous Years Questions Important Questions**Circles – Previous Years Questions**

- In the given figure PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30
**°**. Find ∠PCA.

**[CBSE 2016] [1 Mark]** - Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the similar circle.
**[CBSE 2019] [1 Mark]** - In the given figure, TP and TQ are tangents drawn to the circle with centre at O. If ∠POQ = 115
**°**then ∠PTQ is- 115
**°** - 57.5
**°** - 55
**°** - 65
**°****[CBSE 2020] [1 Mark]**

- 115
- From an external point Q, the length of the tangent to a circle is 5 cm and the distance of Q from the centre is 8 cm. The radius of the circle is
- 39 cm
- 3 cm
39 cm**√**- 7 cm
**[CBSE 2020] [1 Mark]**

- In the given figure AB and CD are common tangents to circles which touch each other at D. If AB = 8 cm, then find the length of CD.

**[CBSE 2020] [1 Mark]** - In the given figure a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q ,R and S respectively. Prove that AB + CD = BC + DA.
**[CBSE 2016] [2 Marks]** - In the given figure, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30
**°**.

**[CBSE 2016] [2 Marks]** - Prove that the lengths of tangents drawn from an external point to a circle are equal.
**[CBSE 2016] [2 Marks]** - In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangents at P. If ∠POQ = 70
**°**then find ∠TPQ.

**[CBSE 2017] [2 Marks]** - In the given figure, find the length of AP, where O is the centre of circle.

**[CBSE 2017] [2 Marks]** - Prove that the lengths of tangents drawn from an external point to a circle are equal.
**[CBSE 2018] [3 Marks]** - In the given figure PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents P and Q intersect at a point T. Find the length TP.
**[CBSE 2019] [3 Marks]** - Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
**[CBSE 2019] [3 Marks]** - In the given figure, XY and MN are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and MN at B. Prove that ∠AOB = 90
**°**.

**[CBSE 2020] [3 Marks]** - In the given figure, AB is the diameter of a circle with centre O and AC is its chord such that ∠BAC = 30
**°**. If the tangent drawn at C intersects extended AB at D, then show that BC = BD.

**[CBSE 2020] [3 Marks]** - Prove that the lengths of the tangents drawn from an external point to a circle are equal.
**[CBSE 2016] [4 Marks]** - In the given figure, two equal circles, with centres O and O
**‘**, touch each other at X. OO**‘**produced meets the circle with centre O’ at A. AC is tangent to circle with centre O, at the point C. O**‘**D is perpendicular to AC. Find the value of DO**‘**/CO.**[CBSE 2016] [4 Marks]** - TP and TQ are two tangents drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
**[CBSE 2017] [4 Marks]** - A model of a traffic signal on the road has a triangular base ABC with ∠A = 90
**°**and with a red circular light within it as shown in the figure. If AB = 12 cm and BC =20 cm and R is the in centre of the triangle ABC, find the area used for the red light.

**[CBSE 2017] [4 Marks]**

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