circle

1. CIRCLE PYQs Class 10
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]

2. CIRCLE PYQs Class 10
1.In the given figure, TP and TQ are tangents drawn to the circle
with centre at O. If ∠POQ = 115° then ∠PTQ is
2.115°
3.57.5°
4.55°
5.65°

3. CIRCLE PYQs Class 10
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]

4. CIRCLE PYQs Class 10
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]

5. CIRCLE PYQs Class 10
1.Prove that the lengths of tangents drawn from an external
point to a circle are equal. [CBSE 2016] [2 Marks]
1.Prove that the lengths of tangents drawn from an external
point to a circle are equal. [CBSE 2018] [3 Marks]

6. CIRCLE PYQs Class 10
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]

7. CIRCLE PYQs Class 10
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.

8. CIRCLE PYQs Class 10
1.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]

9. CIRCLE PYQs Class 10
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

10. CIRCLE PYQs Class 10
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]

11. CIRCLE PYQs Class 10
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]

12. CIRCLE PYQs Class 10

13. CIRCLE PYQs Class 10

14. CIRCLE PYQs Class 10