[" AB and CD to two circles with centres O and O" intery "],[" Prove that the points O,E and O' are collinear."]

In a figure the common tangents, AB and CD to two circles with centers O and O' intersect at E. Prove that the points O, E and O' are collinear.

In a figure the common tangents, AB and CD to two circles with centers O and O' intersect at E. Prove that the points O, E and O' are collinear.

The common tangents AB and CD to two circles with centres O and O' intersect at E between the centres.Prove that the points O,E and O' are collinear.

In Fig common tangents AB and CD to two circles with centres O_1 and O_2 intersect at E. Prove that AB = CD.

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .

Two equal chord AB and CD of a circle with centre O, intersect each other at point P inside the circle. Prove that: BP = DP

Two circles with centres O and O'are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. prove that OA bisects angle BAC.

In the figure,two equal chords AB and CD of a circle with centre O ,intersect each other at E , Prove that AD=CB

Chords AB and CD of a circle with centre O, intersect at a point E. If OE bisects angle AED, prove that chord AB = chord CD.

A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centres O and O'. > Prove that the chords AB and CD, which are intercepted by the two circles, are equal.