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Question

In a triangle ABC, r1ra+r2rb+r3rc=

A
r1+r2+r33
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B
r1+r2+r3
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C
r1+r2+r32
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D
r1+r2+r3s
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Solution

The correct option is D r1+r2+r3s
We know, r1,r2,r3 are the three exradii respectively.
r1ra+r2rb+r3rc
1a[ΔsaΔs]+1b[ΔsbΔs]+1c[ΔscΔs]
Δa[s(sa)s(sa)]+Δb[s(sb)s(sb)]+Δc[s(sc)s(sc)]
Δs(sa)+Δs(sb)+Δs(sc)
1s[r1+r2+r3]
Therefore,
r1ra+r2rb+r3rc=r1+r2+r3s

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