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Question

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

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Solution

Given, BC and BD are the two tangents drawn to the circle with centre O, such that CBD=1200.They are equally inclined to the line segment joining the centre to that point.OBC=OBD=12CBD=600Now, tangent drawn from an external point is perpendicular to the radiusat the point of contact.OCB=ODB=900From ΔOBC, BOC=1800(OCB+OBC)BOC=1800(900+600)BOC=300.Now from right-angled OBC, BCOB=sin300BCOB=12OB=2BC.Hence proved.

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