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

Position of a Point with Respect to Circle

In the figure...

Question

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?

10 c m

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

3 c m

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

17 c m

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

7 c m

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

Open in App

Solution

The correct option is A $10 c m$
Using the property that lenghts of tangents drawn from an external point to circle is same.

$A Q = A R = 5 c m$
Let $C R = C P = x$ and $B P = B Q = y$

Also, $A C = A R - C R =$ $5 - x$ and AB=AQ-BQ= $5 - y$

Perimeter of $Δ A B C = A C + B C + A B$
$\Rightarrow (5 - x) + (5 - y) + x + y$
$\Rightarrow 10 c m$

Suggest Corrections

Similar questions

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.

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. 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

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

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.

Join BYJU'S Learning Program

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?

The correct option is A 10cmUsing the property that lenghts of tangents drawn from an external point to circle is same.AQ=AR=5cmLet CR=CP=x and BP=BQ=yAlso, AC=AR−CR= 5−x and AB=AQ-BQ= 5−yPerimeter of ΔABC=AC+BC+AB⇒(5−x)+(5−y)+x+y⇒10cm

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?