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Question

If in a â–³ABC,r1r2+r2r3+r3r1 is equal to
(where r1,r2 and r3 are the exradii and 2s is the perimeter.)

A
s2
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B
2s2
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C
3s2
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D
4s2
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Solution

The correct option is A s2
r1r2+r2r3+r3r1
=sasb+sbsc+scsa
=2[1(sa)(sb)+1(sb)(sc)+1(sc)(sa)]
By Heron's formula
s(sa)(sb)(sc)[1(sa)(sb)+1(sb)(sc)+1(sc)(sa)]
=[s(sa)(sb)(sc)(sa)(sb)+s(sa)(sb)(sc)(sb)(sc)+s(sa)(sb)(sc)(sc)(sa)]
=s(sc)+s(sa)+s(sb)
=s(3sabc)
=s(3s2s)
=s2

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