CBSE Class 10 Mathematics (Basic) — Circles

12. If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120°$, then ∠PTQ is equal to : (a) 60° (b) 70° (c) 80° (d) 90°

13. In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB = 125°$, then ∠APO is equal to : (a) 25° (b) 65° (c) 90° (d) 35°

25. Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

29. (A) In the given figure, $\triangle ABC$ is a right triangle in which $\angle B = 90^\circ$, $AB = 4\text{ cm}$ and $BC = 3\text{ cm}$. Find the radius of the circle inscribed in the triangle ABC.

29. (B) In the given figure, if a circle touches the side QR of $\triangle PQR$ at S and extended sides PQ and PR at M and N respectively, then prove that : $PM = \frac{1}{2}(PQ + QR + PR)$.