In the given figure, a circle touches the side $B C$ of $△ A B C$ at $P$ and $A B$ and $A C$ produced at $Q$ and $R$ respectively. If $A Q = 15 c m$ , find the perimeter of $△ A B C$ .

30 c m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

24 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

15 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

18 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $30 c m$
$T h e l e n g t h s o f t h e t a n g e n t s, f r o m a p o i n t t o a c i r c l e, a r e e q u a l .$
Therefore AB = AP, BQ = BP, BP = CP
Perimeter = AC + AB + BC = 2(AB) + BP + PC = 2(AB) + 2(BQ) = 2(AQ) = 30 cm

Suggest Corrections

Similar questions

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 ___ $c m$

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.

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.

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

△

ABC at P and sides AB and AC produced at Q and R respectively. What is the perimeter of

△

ABC if AQ = 5 cm?

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

Join BYJU'S Learning Program

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 AQ=15cm, find the perimeter of △ABC.

The correct option is D 30cmThelengthsofthetangents,fromapointtoacircle,areequal.Therefore AB = AP, BQ = BP, BP = CPPerimeter = AC + AB + BC = 2(AB) + BP + PC = 2(AB) + 2(BQ) = 2(AQ) = 30 cm

In the given figure, a circle touches the side $B C$ of $△ A B C$ at $P$ and $A B$ and $A C$ produced at $Q$ and $R$ respectively. If $A Q = 15 c m$ , find the perimeter of $△ A B C$ .

The correct option is D $30 c m$
$T h e l e n g t h s o f t h e t a n g e n t s, f r o m a p o i n t t o a c i r c l e, a r e e q u a l .$
Therefore AB = AP, BQ = BP, BP = CP
Perimeter = AC + AB + BC = 2(AB) + BP + PC = 2(AB) + 2(BQ) = 2(AQ) = 30 cm