Circle Class 10 Important Questions | Circle Class 10 | Circle Class 10 Rapid Revision

1. In Fig. AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP.

2. In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

3. In figure PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is a diameter. If ∠POR = 130° and S is a point on the circle, find angle 1 + angle 2.

4. In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre O. Prove that OP is the right bisector of line segment AB.

5. In the given figure, the sides AB, BC and CA of AABC touch a circle with centre O and radius r at P, Q and R respectively.
Prove that:
(i) AB + CQ = AC + BQ
(ii) Area (∆ABC) = 1/2 (perimeter of A ABC) × r

6. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

7. In the given figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

8. In figure, PQ is a chord of length 16 cm, of a circle of radius 10 cm. The tangents at P and Q intersect at a point T. Find the length of TP.

11. Prove that the tangents drawn at the ends of a diameter of circle are parallel.