Two circles intersect at A and B. From a point P on one of the circles lines PAC and PBD are drawn intersecting the second circle at C and D. Prove that CD is parallel to the tangent at P.

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

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

squareABCD is a parallelogram . Side BC intersects circle at point P . Prove that DC = DP .

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 .

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

O is the origin & also the centre of two concentric circles having radii of the inner & the outer circle as a & b respectively. A line OPQ is drawn to cut the inner circle in P & the outer circle in Q. PR is drawn parallel to the y -axis & QR is drawn parallel to the x -axis. Prove that the locus of R is an ellipse touching the two circles. If the focii of this ellipse lie on the inner circle, find the ratio of inner: outer radii & find also the eccentricity of the ellipse.

No tangent can be drawn from ………… of the circle.

…………….Number of tangents can be drawn from a point inside the circle.

Two circle with centre O and P intersect each other in point C and D. Chord AB of the circle with centre O touches the circle with circle with centre P in Point E. Prove that angleADE+angleBCE= 180^(@)