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Question 4
If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that DBC = 120, prove that BC+BD=BO i.e BO = 2BC.

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Solution

Two tangents BD and BC are drawn from an external point B.

To Prove: BO = 2BC
Given: DBC = 120
Join OC, OD and BO.
Since, BC and BD are tangents.
OC BC and OD BD
We know, OB is an angle bisector of DBC.
OBC=DBO=60
In right angle OBC, cos60=BCOB
12=BCOB
OB = 2BC
Also, BC = BD.
[Tangent drawn from internal point to circle are equal]
OB =BC+BC
OB = BC + BD

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