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.


Answer :

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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