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:
- Radius of incircle is, $r=\frac{\Delta}{s}$
Since,
$$ \Delta=16 \sqrt{2} $$
Now,
$$ \begin{aligned} s & =\frac{6 \sqrt{2}+6 \sqrt{2}+4 \sqrt{2}}{2} \\ & =8 \sqrt{2} \\ r & =\frac{16 \sqrt{2}}{8 \sqrt{2}} \\ & =2 \end{aligned} $$
$$ \therefore \quad r=\frac{16 \sqrt{2}}{8 \sqrt{2}} $$
