A point P is at a distance of 29 cm from the center of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.

A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC, and AC at points D, E, and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.

In the given figure, PA and PB are the tangent segments to a circle with center O. Show that points A, O, B, and P are concyclic.

From an external point P, tangents PA and PB are drawn to a circle with, center O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of ∆PCD.

A circle is inscribed in a ∆ABC touching AB, BC, and AC are P, Q, and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm, find the length of BC.

In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

Prove that the perpendicular at the point of contact of the tangent to a circle passes through the center.

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with center O. If ∠PRQ = 120°, then prove that OR = PR + RQ

In the given figure, O is the center of the circle. PA and PB are tangents. Show that AOBP is a cyclic quadrilateral.

In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.

In the given figure, PQ is a chord of a circle with center O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ.

If the angle between two tangents drawn from an external point P to a circle of radius and center O is 60° then find the length of OP.

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