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Tangents to a Circle Theorem
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Tangents to a Circle:Theorem

Theorem: The lengths of the two tangents drawn from an external point to a circle are equal.
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Example: From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of AB.
Solution: Suppose OP intersects AB at C.
In triangles PAC and PBC, you have
     PA = PB              [Tangents from external point are equal]
     APC = BPC  [PA and PB are equally inclined to OP]
     and, PC = PC      [Common]
so, by SAS-critirion of similarity
    PAC PBC
AC = BC
and ACP = BCP
but, ACP + BCP = 180
ACP = BCP = 90
Hence, OP AB
 
   
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