Prove that the line of centers of two intersecting circles subtends equal angles at the two points of intersection.

Question

Philoid · Accepted Answer

Let two circles with centers as O and O’ intersect each other at point A and B respectively Join OO’.

Now,

In ΔAOO’ and BOO’

O’A = O’B (radius of same circle)

OA = OB (Radius of same circle)

OO’ = OO’ (Common)

Hence, by SSS congruence

ΔOAO’ ΔOBO’

∠OAO’ = ∠OBO’ (By CPCT)

Therefore,

Line of centers of two intersecting circles subtends equal angles at the two points of intersection