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

$\red{solution}$

that OB bisects ∠DBC.

∴∠OBC = ∠OBD = 60°

In ∆OBC,

∠OBC = 60°, ∠OCB = 90°

∠COB + ∠OBC +∠OCB = 180° [Angle sum property of triangle]

∠COB + 60° + 90° = 180°

∠COB = 180° – 150° = 30° In a ΔOBC,

sin ∠COB = BC / BO

sin 30° = BC / BO

1 / 2 = BC / BO

BO = 2BC.