You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Tangent from an External Point Are Equal

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.

__

Open in App

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

Suggest Corrections

Similar questions

Q. In the given figure, a circle touches the side

B C

△ A B C

P

and

A B

and

A C

produced at

Q

and

R

respectively. If

A Q = 15 c m

, find the perimeter of

△ A B C

In the given figure, a circle touches the side BC of $△$ ABC at P and AB and AC produced at Q and R respectively. If $A Q = 15 c m,$ then the perimeter of $△$ ABC is ___ $c m$

Q. A circle touches the side BC of ∆ABC at P and touches AB and AC produced at Q and R, respectively, as shown in the given figure. Show that

A Q = \frac{1}{2} \times (perimeter of ∆ A B C) .

Figure

Q. A circle touches the side BC of

Δ

ABC at P and touches AB and AC produced at Q and R respectively.

I f A Q = 5 c m

, then find the perimeter of

Δ

ABC

Q. In fig., a circle touches the side BC of

Δ A B C

at P and touches AS and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of

Δ A B C

Join BYJU'S Learning Program

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