In the given figure, MN is the common chord of two intersecting circles and AB is their common tangent.

Prove that the line NM produced bisects AB at P.

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that: (i) tangent at point P bisects AB (ii) angle APB=90^(@)

In the given figure, O is the centre of the circle. If chord AB= chord AC, OP bot AB and OQ bot AC , show that: PB= QC

In the given figure AB is the diameter and AC is the chord of a circle such that /_BAC=30^(@) . The tangent at C intersects AB produced at D. Prove that :BC=BD.

The figure shows two concentric circles and AD is a chord of larger circle. Prove that : AB = CD.

In the given figure, there are two circles with centers A and B. The common tangent to the circles touches them, respectively,at P and Q. AR is 40cm and AB is divided by the point of contact of the circles in the ratio 5:3 The radius of the circle with center B is

The length of the common chord of two circles of radii r_1 and r_2 which intersect at right angles is

The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm. Calculate the distance between their centres.

The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm, calculate the distance between their centres.

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.