Question

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

Answer 1

Let two circles having their centres as O and O' intersect each other at point A and B respectively. Let us join OO'.

In ΔAOO' and BOO',

OA = OB (Radius of circle 1)

O'A = O'B (Radius of circle 2)

OO' = OO' (Common)

ΔAOO' ≅ ΔBOO' (By SSS congruence rule)

∠OAO' = ∠OBO' (By CPCT)

Therefore, line of centres of two intersecting circles subtends equal angles at the two points of intersection.