Let two circles with centers as O and O’ intersect each other at point A and B respectively Join OO’.
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
∠OAO’ = ∠OBO’ (By CPCT)
Line of centers of two intersecting circles subtends equal angles at the two points of intersection.
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