Refer to the image?!

enter image source here
Prove:Area of the triangle=R*S;
where,
R=radius of the incircle,
and,
S=Semi-perimeter of the triangle,
which is,Perimeter of the triangle/2

1 Answer
Feb 13, 2018

"see explanation"

Explanation:

"this is going to be 'tricky' without diagrams but here goes"

"from the centre of the circle draw line segments to each"
"vertex of the triangle"

"this 'splits' the main triangle into 3 triangles "

"draw in the 2 remaining radii to the point of contact with"
"the sides of the triangle similar to the one shown in the image"

"the sum of the areas of the 3 triangles are equal to"
"the area of the main triangle"

"let the 3 sides be "b_1,b_2" and "b_3

rArr"area "=1/2Rb_1+1/2Rb_2+1/2Rb_3

color(white)(rArr"area ")=1/2R(b_1+b_2+b_3)

color(white)(rArr"area ")=Rxx1/2(b_1+b_2+b_3)

color(white)(rArr"area ")=RS