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Question

In figure, a circle touches the side BC of ABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter (in cm) of ABC.


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Solution

We know that

AQ = AR

AQ = AC + CR

But CR = CP

AQ = AC + CP    …..(i)

Also AQ = AB + BQ

But BQ = BP

AQ = AB + BP     .….(ii)

Adding equations (i) and (ii)

2AQ = AC + CP + BP + AB

2AQ = Perimeter of ABC

Perimeter of ABC = 2 × 5 = 10 cm

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