Asked by Rishabh1 | 25th Jun, 2009, 09:42: PM
Let ABCD be the parallelogram which touches a circle with sides AB,BC,CD,DA touching the circle at P,Q,R,S respectively.
So, using the fact that lengths of tangent segments drawn from an external point to a circle are equal , we get,
Adding, we get
So we have,
but AB=CD and AD=BC..(opp sides of a paralelogram)
thus we have proved that ABCD is a parallelogram with one pair of adjacent sides equal , so ABCD is a rhombus by definition.
Answered by | 25th Jun, 2009, 10:17: PM
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