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In Δ AOP and Δ AOC ,
AO = AO [ Common ]
OP = OC [ Radius ]
AP = AC [ Tangent from a single point ]
Δ AOP ≅ Δ AOC [ S.S.S ]
∠POA = ∠AOC [ c.p.c.t ]
Similarly :
Δ BOC ≅ Δ OQB
∠COB = ∠BOQ [ c.p.c.t ]
Add both c.p.c.t :
∠POA + ∠AOC + ∠COB + ∠BOQ = 180
[ angles on a straight line ]
⇒ 2 ∠POC + 2 ∠COB = 180
⇒ ∠POC + ∠COB = 90
⇒ ∠AOB = 90
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