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

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

Two tangents are draw from an external point A to the cirle with centre at O. If they touch the circel at the point B and C then prove that AO is the perpendicular bisector of BC.

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.

Two circles intersect each other. Radius of both the circles is 10cm in length and length of the common chord is 16cm. What is the distance between the centres of the two circles?

Prove that if any straight line passing through the centre of a circle bisects any chord, which is not a diameter, then the straight line will be perpendicular on that chord.

Prove analytically that the straight line joining the middle point of a chord of a circle with the centre is perpendicular to the chord.

The radii of two circles are 10 cm and 5 cm and the distance between their centres is 13 cm. Find the length of the direct common tangent to the two circles.

Two chords AB and CD of a circle with centre O intersect each other at the point P. prove that AOD+ angle BOC = 2 angle PBC . If angle BOC are supplementary to each other, then prove that the two chords are perpendicular to each other.

Two chords AB and CD of a circle intersect at the point P, which is inside the circle and O is the centre of the circle. If angleAOC = 55^@ , and angleBOD =45^@ , then angleAPC =