Question

Please solve it. A kind and humble request.

Answer 1

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))