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If the perimeter of a triangle and the d...

If the perimeter of a triangle and the diameter of an ex-circle are equal , then the triangle is

A

right angled isosceles

B

right angled

C

equilateral

D

isosceles

Text Solution

Verified by Experts

Let ABC be the triangle such that
`a+b+c=2r_(1)`
`rArr2R(sinA+sinB+sinC)=8RsinA/2cosB/2cosC/2`
`rArr2Rxx4cosA/2cosB/2cosC/2=8RsinA/2cosB/2cosC/2`
`rArrcosB/2cosC/2(cosA/2-sinA/2)=0`
`rArrcosA/2-sinA/2=0rArrtanA/2=1rArrA=pi/2`
Hence, the triangle ABC is right angled at A.
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