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Standard IX

Mathematics

Lengths of Tangents Drawn from External Point

In the given ...

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.

__

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Solution

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

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 ΔABC = 2 × 15 = 30 cm

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.

__

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