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

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

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Consider the following diagram

In ΔPOO’ and ΔQOO’

OP = OQ          (Radius of circle 1)

O’P = O’Q        (Radius of circle 2)

OO’ = OO’        (Common arm)

So, by SSS congruency, ΔPOO’ ≅ ΔQOO’

Thus, ∠OPO’ = ∠OQO’ (proved).

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