Question

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

Answer 1

Given : AB and CD are common tangents to the circles with centre O and O' intersecting at E.
We know that tangents drawn from an exterior point are equally inclined to the segment joining the centre to that point

=> angle AEO = angle CEO

or

EO is the angle bisector of angle AEC ........(1)

and angle BEO' = angle DEO'

or 

EO' is the angle bisector of angle BED ........(2)

but angle AEC = angle BED .............(3)

from (1), (2) and (3) we can conclude that Eo' coincides with EO 

or

E, O', O are coillinear.

2528e7a02183a5db91599d0bb4ac5830.docx

Answer 2

Hi there here's your answer

Hope it helps