In a ABC- if 1- r1r2 1- r1r3 - 2- Then ABC is

The correct option is A Right angled ( 1 r_1r_2) ( 1 #10;r_1r_3) = ( 1 s bs a) ( 1 s cs a #10;) = 2 b as a·c as a =2 2(s a)^2 = (b a)(c a ...

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AM,GM,HM Inequality

In a ABC, i...

Question

In a $△ A B C$ , if $(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2$ . Then $△ A B C$ is

Equilateral

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Isosceles

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Right angled

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Acute angled

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Solution

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A B C

(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2

△ A B C,

(\frac{1}{r_{1}} + \frac{1}{r_{2}}) (\frac{1}{r_{2}} + \frac{1}{r_{3}}) (\frac{1}{r_{3}} + \frac{1}{r_{1}}) = \frac{K R^{3}}{a^{2} b^{2} c^{2}},

K

(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2,

(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2

(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2,

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