Question

solve the following questions​

Answer 1

Answer:

Join AP, BP, CP, PL, PM and PN

PL = PM = PN = r    (radius is given as r)

Now, Ar(ΔABC) = Ar(ΔAPB) + Ar(ΔBPC) + Ar(ΔAPC)

=> Ar(ΔABC) = $\frac{1}{2} (AB)(r) + \frac{1}{2} (BC)( r) + \frac{1}{2} (AC)(r)$               (Area of a Δle = $\frac{1}{2} bh$)

=>  Ar(ΔABC) = $\frac{1}{2} r (AB + BC + AC)$

=> Ar (ΔABC) = $\frac{1}{2} (AB + BC + AC) r$

Hope it helps...

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