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Construction of Incircle

If sides of a...

Question

If sides of a triangle are in the ratio $7 k, 8 k, 9 k$ and the radius of the incircle is $3 \sqrt{5}$ , the $k$ is equal to

A

2

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B

1

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C

3

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D

4

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Solution

The correct option is B 3
$s = \frac{7 k + 8 k + 9 k}{2} = 12 k$
$Δ = \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{12 k \cdot 5 k \cdot 4 k \cdot 3 k} = 12 \sqrt{5} k^{2}$

$r = \frac{Δ}{s} ⟹ 3 \sqrt{5} = \frac{12 \sqrt{5} k^{2}}{12 k} ⟹ k = 3$

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