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Circle Tangent: Example
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Example: A circle touches all the four sides of a quadrilateral PQRS, Prove that:
PQ + RS = QR + SP
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Solution: Since tangents drawn from an exterior point to a circle are equal in length.
PA = PD     ....(i)
QA = QB     ....(ii)
RC = RB     ....(iii)
and, SC = SD     ....(iv)
Adding equations (i), (ii), (iii) and (iv), we get
PA + QA + RC + SC = PD + QB + RB + SD
(PA + QA) + (RC + SC) = (PD + SC) + (QB + RB)
= PQ + RS = PS + QR 
Hence, PQ + RS = QR + SP
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