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Step-by-step explanation:
We can divide ΔABC into three triangles respectively,
ΔAPB, ΔBPC and ΔAPC
Therefore Ar(ΔABC) = Ar(ΔAPB) + Ar(ΔBPC) + Ar(ΔAPC)
= (1/2 * AB * r) + (1/2 * BC * r) + (1/2 * AC * r)
= 1/2(AB + BC + AC) * r
Hence Proved
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