Q. 84.8( 4 Votes )

# Two tangent segments BC and BD are drawn to a circle with center O such that ∠CBD = 120°. Prove that OB = 2BC.

Given : A circle with center O , BC and BD are two tangents such that CBD = 120°

To Proof : OB = 2BC

Proof :

In BOC and BOD

BC = BD

[Tangents drawn from an external point are equal]

OB = OB

[Common]

OC = OD

[Radii of same circle]

BOC BOD [By Side - Side - Side criterion]

OBC = OBD

[Corresponding parts of congruent triangles are congruent]

OBC + OBD = CBD

OBC + OBC = 120°

2 OBC = 120°

OBC = 60°

In OBC

OB = 2BC

Hence Proved !

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