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Question

If r1,r2 and r3 are thecorresponding exradii of a ΔABC and r is the inradiiof the same triangle, then1r1+1r2+1r3=1r

A
True
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B
False
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Solution

The correct option is A True
We know that,r1= Δsa , r2= Δsbr3= Δsc , r= Δs1r1+1r2+1r3=1Δsa+1Δsb+1Δsc= sa+sb+scΔ= 3s(a+b+c)Δ= (3s2sΔ)=sΔ=1r

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