Question

Two non-intersecting circles have 2 intersecting common tangents. Prove that the two centres and the point of intersection are co-linear.

Answer 1

Here AB and CD are extended then they are intersecting at P.

Length of two tangents drawn from external point to a circle are equal.

AP = CP ----------(1)
BP = DP ----------(2)

Substracting (2) from (1) we get

AP - BP = CP - DP

∴ AB = CD