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Question

A circle touches two of the smaller sides of a ΔABC(a<b<c) and has its center on the greatest side. Then the radius of the circle is

A
abc2
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B
abc2
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C
2Δa+b
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D
None of these
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Solution

The correct option is C 2Δa+b

Let O be the center and r be the radius of the circle.
Then
areaΔBOC +area ΔAOC =areaΔABC
(a+b)r2=s(sa)(sb)(sc)
r=2s(sa)(sb)(sc)a+b=2Δa+b

283964_141847_ans_8fe15082a03240db84b731c9a79f78bd.png

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