In the given figure, a circle touches the side BC of ΔABC at P and AB and AC pr

Question

In the given figure, a circle touches the side BC of $Δ$ ABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of $Δ$ ABC.

Options:

Answer: Option A
:

We know that

AQ = AR

AQ = AC + CR

But CR = CP

Therefore 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 ΔABC

Perimeter of $Δ$ ABC = 2 $\times$ 15 = 30 cm

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