Radius of the incircle of the triangle $P Q R$ is?

4

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

5

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

6

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

8

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

Open in App

Solution

The correct option is C $5$
From the above coordinates, the sides of the triangle will be
$Q R = 20$ units
$P R = 15$ units
and $P Q = 25$ units.
The coordinates of the incentre can be given by the following
$x = \frac{20 (- 8) + 15 (- 15) + 25 (1)}{20 + 15 + 25}$
$= - 6$
Similarly
$y = \frac{20 (5) + 15 (- 19) + 25 (- 7)}{20 + 15 + 25}$
$= - 6$
The equation of PR will be given by
$(y + 7) = \frac{- 12}{9} (x - 1)$
$\Rightarrow 9 y + 63 = - 12 x + 12$
$\Rightarrow 3 y + 21 = - 4 x + 4$
$\Rightarrow 4 x + 3 y + 17 = 0$
Now the inradius will be the distance of $(- 6, - 6)$ from the line $4 x + 3 y + 17 = 0$
$= | \frac{- 24 - 18 + 17}{5} |$
$= 5$ units

Suggest Corrections

Similar questions

Δ

Δ

Construct a $Δ$ PQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.

P Q R

450

{in}^{2}

150

P Q R

Construct a $Δ$ PQRwith QR = 8 cm, PQ = 6 cm, PR = 4 cm. Construct the incircle of the triangle and find the radius of the incircle.

Join BYJU'S Learning Program