Prove that the two different circle can never intersect at more that two point .

In two circles , one circle passes through the centre O of the other circle and they intersect each other at the points A and B . A straight line passing through A intersect the circle passing through O at the point P and the circle with centre at O at the point R . BY joining P , B and R , B prove that PR= PB.

Can two different equipotential surfaces intersect each other?

How many maximum number of common tangents of two circles can be drawn intersecting at two different points ?

Each of the two equal circles passes through the centre of the other and the two circles intersect each other at the points. A and B.If a straight ine through the point A intersects the two circles at points C and D prove that Delta BCD is an equilateral triangle.

The two circles with centre X and Y intersect each other at the points A and B, A joined with the mid -point S of XY and the perpendicular on SA through the point A is drawn which intersect the two circles at the point P and Q .Prove that PA = AQ.

P is any point on diameter of a circle with centre O.A perpendicular drawn on diameter at the point O intersects the point O intersects the circle at the point Q. Extended QP intersects the circle at the point R.A tangent drawn at the point R intersects extended OP at the point S. Prove theat SP=SR. [GP-X]

Two tangents drawn at the point A and B on a circle intersect each other at the point P. If angle APB=60^(@), then anglePAB=

A straight line intersects one of the two concentric circles at the points A and B and other at the points C and D. Prove that AC = BD.

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST