In the given figure, triangle ABC is circumscribing a circle. Find the length of BC, if AF=3 cm, FB=4 cm and AC= 9 cm

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the parallelogram circumscribing a circle is a rhombus.

In Figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If angle POQ = 70°, then angleTPQ is equal to

In Figure 2, AB and AC are tangents to the circle with centre O suchthat angle BAC = 40°. Then angle BOC is equal to

In Figure 5, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of $\Delta PQR=189c{m}^2$, then find the lengths of sides PQ andPR.

In Figure 3, a circle touches all the four sides of a quadrilateral ABCDwhose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of side AD.

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

From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is

Prove that the length of the tangents drawn from an external point to a circle are equal.