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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Answer 1

We know that

AQ = AR

AQ = AC + CR

But CR = CP

$\therefore$ AQ = AC + CP …..(i)

Also AQ = AB + BQ

But BQ = BP

$\therefore$ AQ = AB + BP .….(ii)

Adding equations (i) and (ii)

2AQ = AC + CP + BP + AB

2AQ = Perimeter of $△$ABC

Perimeter of $△$ABC = 2 $\times$ 5 = 10 cm