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.

Two circles intersect each other in point A and B . Secants through A and B intersect circles in C, D and M, N as shown in the figure prove that : CM||DN

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .

In the adjoining figure circles with centres A and C touch internally at point T . Line AB is tangent to the smaller circle at point P . Point B lies on the bigger circle. Radii are 16 cm and 6 cm . Find AP.

In the adjacent figure lines PQ and RS intersect each other at point O. If anglePOR : angleROQ = 5: 7, find all the angles.

In the adjoining figure, ray PQ touches the circle at point Q. Line PRS is a secant, If P=12, PR=8 then PS and RS

Prove that a line cannot intersect a circle at more two points .

In the adjoining figure bisectors of angleBand angleC intersect each other in point X. Line AX intersects side BC in point Y. AB=5, AC=4, BC=6 "then find" (AX)/(XY) .

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