A circle with centre P is inscribed in the side AB, side BC and side AC touch the circle at point L, M and N respectively. Radius of the circle is r. Then area of side AB, side BC and side AC touch the circle at point L, M and N respectively. Radius of the circle is r. Then area of is

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\frac{1}{2} \times r \times (AB + BC + CA)

\frac{1}{2} \times (AB + BC + CA)

\frac{1}{2} \times AB \times BC \times CA

None of These

answer is A.

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Detailed Solution

Let O be the centre of circle
join OL, ON and OM
Join OA, OB and OC
Clearly

and OM = ON = OL = r (radius)
Now

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