If in a triangle `(1-(r_1)/(r_2))(1-(r_1)/(r_3))=2` then the triangle is right angled (b) isosceles equilateral (d) none of these

Options

A. right angled
B. isosceles
C. equilateral
D. none of these

Answer

A

Explanation

We have `(1-(s-b)/(s-a)) (1-(s-c)/(s-a)) = 2`
or `2(b-a) (c-a) = 4 (s-a)^(2)`
or or `2(bc-ac -ab +a^(2)) = (2s-2a)^(2)`
or `a(bc-ac-ab+a^(2)) = (b+c -a)^(2)`
or `a^(2) = b^(2) + c^(2)`
Hence, triangle is right angled