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Question

if r1=r2+r3+r, then the Δ is

A
Equilateral
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B
Isosceles
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C
Right angled
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D
None of these
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Solution

The correct option is D Right angled
r1=r2+r3+r

r1r=r2+r3

ΔraΔr=Δrb+Δrc

rr+ar(ra)=rb+rc(rb)(rc)

ar(ra)=a+b+cbc(rb)(rc)

ar(ra)=a(rb)(rc)

1r(ra)=1(rb)(rc)

(rb)(rc)=r(ra)

r2brcr+bc=r2ar

(abc)r+bc=0

(b+ca)r=bc

(b+ca)(a+b+c)2=bc

(b+c)2a2=2bc

(b+c)22bc=a2

b2+c2=a2

The triangle is a right triangle.

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