Question

in the given figure a square is inscribed in a circle with centre O find angle BOC ,angle OCB, angle COD, angle BOD​

Answer 1

Given : a square is inscribed in a circle with centre O

To Find : ∠BOC ,∠OCB, ∠COD, ∠BOD​

Solution:

AB = BC = BC = AD   ( equal sides of Square)

Angle subtended by equal chord are equal

=> ∠AOB = ∠BOC = ∠COD, ∠AOD

∠AOB + ∠BOC + ∠COD + ∠AOD =  360°

=> ∠AOB = ∠BOC = ∠COD = ∠AOD = 90°

∠BOC = ∠COD  =  90°

∠BOD​ = ∠BOC+ ∠COD = 90° + 90° = 180°

=> BD is diameter as center lies on BD

in ΔBOC

∠OBC = ∠OCB  as OB = OC  =  radius

=> ∠OBC +  ∠OCB + ∠BOC = 180°

=> ∠OBC +  ∠OCB + 90° = 180°

=> ∠OBC +  ∠OCB = 90°

∠OBC = ∠OCB

=> ∠OCB = 45°

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