Chhattisgarh Board Solutions for Exercise 24: Exercise 5

From a point $P$, which is at a distance of $10 \mathrm{cm}$ from the centre of the circle, the length of the tangent segment is $8 \mathrm{cm}$. Find the radius of the circle.

In the figure, $\angle POQ=100°$, $AP$ and $AQ$ are tangents. Find the value of $\angle PAO$.

Prove that the tangents drawn at the endpoints of a diameter of a circle are parallel to each other.

A circle touches all the sides of a quadrilateral $ABCD$. Prove that $AB+CD=BC+DA$.

Prove that the angle between two tangents drawn from the same external point is supplementary to the angle subtended at the centre by the chord which is formed by joining the contact points of the tangents.

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.