Please solve it. A kind and humble request.
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Construction: Draw BP & CP
Proof:PM=PL=P;=r..(I)
AREA OF A TRIANGLE = 1/2 * HEIGHT * BASE
In triangle APB,
PL is height and AB is base
Area of triangle APB = 1/2*PL*AB.. ( II.)
In triangle BPC,
PM is height and BC is base
Area of triangle BPC =
1/2*PM*BC.. (III)
In triangle APC
PN is height and AC is base
Area of triangle APC = 1/2*PN*AC.. (IV)
Triangle APB, APC, and BPC together constitute triangle ABC
FROM (I), (II), (III)
A(ABC) = A(APB) + A(APC) + A(BPC)
A(ABC) = 1/2*PL*AB + 1/2*PM*BC + 1/2*PN*AC
A(ABC) = 1/2*r ( AB + BC + AC).. (from(I))
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