In the figure AL, BM and BC are the tangents on the circle at point L, M and P respectively. If `AB= 1 cm` and `angleABC =60^@` find the radius of the circle.

In the given figure, BC,BA and AC are tangents to the circle touching the circle at D,E and F respectively. If BD=30cm, CD=7cm and angleA=90^@ , find the radius of the circle.

In the given figure ,AB,BC and AC touch the circle at L,M and N respectively .If angleB=70^(@) and angleC=60^(@) ,then the measure of angleLON is :

In the adjoining figure, O is the centre of the circle and AB is its diameter. If AC=8 cm and BC= 6cm, then find the radius of the circle.

In the adjoining figure, O is the centre of the circle and AB is its diameter. If AC=8 cm and BC= 6cm, then find the radius of the circle.

P is a point out side a circle, which is 13 cm from the centre. A line drawn from point P intersects the circle at point A and B such that PA = 9 cm and AB = 7 cm. Then find the radius of the circle.

In the following figure, point ‘A’ is the centre of the circle. Line MN is tangent at point M. If AN = 12 cm and MN = 6 cm, determine the radius of the circle.

A right triangle ABC, right angled at A, is circumscribing a circle. If AB = 8 cm and BC = 6 cm, find the radius of the circle.

In the given figure, TB is a chord which passes through the centre of the circle. PT is a tangent to the circle at the point T on the circle. If PT = 10 cm, PA = 5 cm and AB = x cm. then the radius of the circle is:

In the given figure AP and AQ are tangents to the circle with centre O. BC is tangent at point R on it. If OA=17 cm and radius of the circle =8cm, find the perimeter of the triangle ABC.

In the given figure, AB, BC and Ac are tangents to the circle at P,Q and R. If AB = AC, show that Q is the mid-point of BC.