Refer to the image?!
![enter image source here]()
Prove:Area of the triangle=R*S=R⋅S ;
where,
R=R= radius of the incircle,
and,
S=S= Semi-perimeter of the triangle,
which is,Perimeter of the triangle/2/2
Prove:Area of the triangle
where,
and,
which is,Perimeter of the triangle
1 Answer
Explanation:
"this is going to be 'tricky' without diagrams but here goes"this is going to be 'tricky' without diagrams but here goes
"from the centre of the circle draw line segments to each"from the centre of the circle draw line segments to each
"vertex of the triangle"vertex of the triangle
"this 'splits' the main triangle into 3 triangles "this 'splits' the main triangle into 3 triangles
"draw in the 2 remaining radii to the point of contact with"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 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 sum of the areas of the 3 triangles are equal to
"the area of the main triangle"the area of the main triangle
"let the 3 sides be "b_1,b_2" and "b_3let the 3 sides be b1,b2 and b3
rArr"area "=1/2Rb_1+1/2Rb_2+1/2Rb_3⇒area =12Rb1+12Rb2+12Rb3
color(white)(rArr"area ")=1/2R(b_1+b_2+b_3)⇒area =12R(b1+b2+b3)
color(white)(rArr"area ")=Rxx1/2(b_1+b_2+b_3)⇒area =R×12(b1+b2+b3)
color(white)(rArr"area ")=RS⇒area =RS
