Prove that “ the tangent drawn from an external point to a circle are eqaul”.
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Explanation:
Given - A circle with centre O .
Take a point P.
Take two tangents from P - AP and BP
To prove - AP = BP
Proof - Now join OP
In triangle AOP and triangle BOP,
AO = BO ( radii of same circle )
OP = OP ( common )
angle OAP = angle OBP ( Each = 90 )
( Tangents are perpendicular to radius of a circle )
Therefore , triangle AOP is congruent to triangle BOP ( by RHS congruency )
By CPCT , AP= BP
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