In a triangle 1- r 1- r 21- r 1- r 3-2 then the triangle isA- No such triangle existsB- isoscelesC- right angledD- equilateral

The correct option is C right angled Given, (1 r_1/r_2 ) (1 r_1/r_3 )=2 ∴ (1 s b/s a ) (1 s c/s a )=2 ⇒(b a)(c a)/(s a)^2=2 ⇒ a^2=b^2+c^2 Hence, triangle is a ...

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Byju's Answer

Standard XII

Mathematics

Cosine Rule

In a triangle...

Question

In a triangle $(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2$ then the triangle is

right angled

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isosceles

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equilateral

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No such triangle exists

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Solution

The correct option is A
right angled

Given, $(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2 ∴ (1 - \frac{s - b}{s - a}) (1 - \frac{s - c}{s - a}) = 2 \Rightarrow \frac{(b - a) (c - a)}{(s - a)^{2}} = 2 \Rightarrow a^{2} = b^{2} + c^{2}$

Hence, triangle is a right angled triangle

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In a triangle (1−r1r2)(1−r1r3)=2 then the triangle is

The correct option is A right angled Given, (1−r1r2)(1−r1r3)=2∴(1−s−bs−a)(1−s−cs−a)=2⇒(b−a)(c−a)(s−a)2=2⇒a2=b2+c2 Hence, triangle is a right angled triangle

In a triangle $(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2$ then the triangle is

The correct option is A
right angled

Given, $(1 - \frac{r_{1}}{r_{2}}) (1 - \frac{r_{1}}{r_{3}}) = 2 ∴ (1 - \frac{s - b}{s - a}) (1 - \frac{s - c}{s - a}) = 2 \Rightarrow \frac{(b - a) (c - a)}{(s - a)^{2}} = 2 \Rightarrow a^{2} = b^{2} + c^{2}$

Hence, triangle is a right angled triangle