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If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that angle DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.

1 Answer

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by (48.8k points)
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Best answer

According to the question,

By RHS rule,

ΔOBC and ΔOBD are congruent

By CPCT

∠OBC and ∠ OBD are equal

Therefore,

∠OBC = ∠OBD =60°

In triangle OBC,

cos 60°=BC/OB

½ =BC/OB

OB=2BC

Hence proved

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