Question

two tangent segments BC and BD are drawn to a circle with Centre O such that angle CBD equals to 120 degree prove that OB = 2BC​

Answer 1

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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