Answer :

Construct Line OC = radius

OP = OQ = OC = radius

OC∥AP and AC∥OP and

Thus AP = OP = radius

As AP = OP and ∠P = 90°

ΔOAP is isosceles triangle

∴ ∠ PAO = ∠POA = 45°

Also ∠ PAC = 90°

∠OAC = 45° ---1

Also AB is perpendicular to OC

∠OCA = 90°

In ΔAOC

∠OCA + ∠OAC + ∠COA = 180°

45 + 90 + ∠COA = 180°

∠COA = 45°

Similarly

∠BOC = 45°

∴ ∠AOB = 90°

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