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If in a triangle (1-(r(1))/(r(2)))(1-(r(...

If in a triangle `(1-(r_(1))/(r_(2)))(1-(r_(1))/(r_(3)))=2`, then the triangle is

A

right angled

B

isosceles

C

equilateral

D

none of these

Text Solution

Verified by Experts

We have,
`(1-(s-b)/(s-a))(1-(s-c)/(s-a))=2`
`rArr2(b-a)(c-a)=4(s-a)^(2)`
`rArr2(bc-ac-ab+a^(2)) =(2s -2a)^(2)`
`rArra^(2)=b^(2)+c^(2)`
`rArrDelta` ABC is right angled at A.
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