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Question

In a triangle ABC, C=90,r and R are the in-radius and circum-radius of the triangle ABC respectively, then 2(r+R) is equal to

A
b+c
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B
c+a
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C
a+b
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D
a+b+c
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Solution

The correct option is C a+b
The figure below represents the triangle.
In the above figure, OECD is a square since all angles are right angle.
BE=ar
AD=br
Also, tangents drawn from an external point are equal.
Therefore, BF=BE
and AF=AD

ar+br=2R
2(r+R)=a+b

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