Question

Prove that 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 intersect each other at point A and B respectively. Let us join O.

In ΔAO and BO,

OA = OB (Radius of circle 1)

A = B (Radius of circle 2)

O = O (Common)

ΔAO ≅ ΔBO (By SSS congruence rule)

∠OA = ∠OB (By CPCT)

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