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Question

A circle touches two of the smaller sides of a ABC(a<b<c) and has its center on the greatest side. 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 D 2Δa+b
Let O be the centre and r be the radius of the circle.
Then, area (AOC)+ area (AOC)= area (ABC)
(a+b)r2=s(sa)(sb)(sc)
r=2s(sa)(sb)(sc)a+b=2a+b
where, s=a+b+c2

474974_254534_ans_e9779448e656492ca84e19e1e12b69ca.png

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