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

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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 ΔBOO',

OA = OB (Radius of circle 1)

O'A = O;B (Radius of circle 2)

OO' = OO' (Common)

Δ AOO' ≅ 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.

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