Question

a circle touches the side of a quadrilateral ABCD and P Q R S respectively show that the angle subtended at the centre by a pair of opposite sides are supplementary

Answer 1

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∠AOD + ∠BOC = 180°

∠AOB + ∠COD = 180°

Now the area OSDR = ΔODS x ΔODR

∡1 + ∡4 + ∡5 + ∡8 = 180°

∡2 + ∡3 + ∡6 + ∡7 = 180°

∠AOD + ∠BOC = 180° (∡1 + ∡4 + ∡5 + ∡8 = 180°)

∠AOB + ∠COD = 180° (∡2 + ∡3 + ∡6 + ∡7 = 180°)

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