In the adjoining figure, O is the centre of the circle XY is a diameter. OY = YR, O-Y-R, RZ is a tangent through Z.A thangent through the point Y intersects RZ in Q and XZ in P
prove that : `DeltaPQZ` is an equilateral triangle.

O is the centre of the circle QOR is diameter. PQ is tangent to the circle. Given P hat(O)R = 130^(@) . Find O hat(P)Q .

In the adjoining figure, O is the centre and seg AB is a diameter. At point C on the circle, the tangent CD is drawn. Line BD is tangent at B . Prove that seg OD || seg AC.

In the adjoining figure point O is the centre of the circle . Line PB is a tangent and line PAC is a secnt. Find Paxx PC if OP = 25 and radius is 7 .

In the adoining figure, A is the centre of the circle. Poin D is in the exterior of the circle. Line DP and Line DQ are tangents at points at P and Q respectively. Prove that DP=DQ.

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

In the adjoining figure, seg EF is the diameter of the circle with centre H . Line DF is tangent at point F . If r is the radius of the circle, then prove that DExxGE=4r^(2) To Prove : DExxGE=4r^(2)

In figure, O is the centre of the circle with radius 5 cm. T is a point such that OT=13 cm and OT intersects the circle E, if AB is the tangent ot the circle at E, find the length of AB.

In the adjoining figure, O is the centre of the circle. From point R, seg RM and RN are tangent segments drawn which touch the circle at M, N . If OR = 10 cm, radius of the circle = 5 cm, then find (i) the length of each tangent segment (ii) Measure of angleMRO (iii) Measure of angleMRN

In the adjoining figure, two circles intersect each other at points M and N . Secants drawn from points M and N intersect cirecls at point R, S, P and Q as shown in the figure.