Two circles intersect each other at P externally. The straight QR touches the circle at two points Q and R. Prove that `/_QPR = 1` right angle.

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

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.

If two circles intersect each other, then the number of their common tangents will be

Two circles touch each other at the point R. PQ is a common tangent to both the circle which touches the circle at the points P and Q. Then anglePRQ=

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .

Two circles with centres A and B touch each other internally. Another circle touches the larger circle internally at the point X and the smaller circle externally at the point Y. If O be the centre of that circle, prove that (OA + BO) is constant.

Laxmi has drawn two circles which intersect each other at O externally. If PQ and RS be two parallel diameters of trhe circles, then prove that the points P, O and S are collinear.

Two tangents are drawn from an external point A of the circle with centre at O which touches the circle at the points B and C. Prove that AO is the perpendicular bisector of BC.