The Total solution for NCERT class 6-12
Consider the followingdiagram
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).