Properties of Triangles 3 Question 6

6. The radius of the incircle of $\triangle P Q R$ is

(a) 4

(b) 3

(c) $\frac{8}{3}$

(d) 2

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Answer:

Correct Answer: 6. (d)

Solution:

  1. Radius of incircle is, $r=\frac{\Delta}{s}$

Since,

$$ \Delta=16 \sqrt{2} $$

Now,

$$ \begin{aligned} s & =\frac{6 \sqrt{2}+6 \sqrt{2}+4 \sqrt{2}}{2} \\ & =8 \sqrt{2} \\ r & =\frac{16 \sqrt{2}}{8 \sqrt{2}} \\ & =2 \end{aligned} $$

$$ \therefore \quad r=\frac{16 \sqrt{2}}{8 \sqrt{2}} $$



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