Question

Find the radius of a circle inscribed in a 5 12 13 triangle

Answer 1

semiperimeter of triangle= 5+12+13/2

=15

area =

$\sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

=3*5*1.414

= 21.21sq.cm

after this we will join each corner of triangle with center of circle o.

then the triangle will divide into three parts

name these triangles as AOB,AOC and BOC

then area of triangle ABC= area(AOC+AOB+BOC)

$21.21 = \frac{1}{2}r (5 + 12 + 13)$

{r=radius of circle}

therefore radius = 1.40 cm