If #a, b and c# are the three sides of a triangle then the radius of its in center is given by
#R=Delta/s#
Where #R# is the radius #Delta# is the are of the triangle and #s# is the semi perimeter of the triangle.
The area #Delta# of a triangle is given by
#Delta=sqrt(s(s-a)(s-b)(s-c)#
And the semi perimeter #s# of a triangle is given by
#s=(a+b+c)/2#
Here let #a=8, b=7 and c=6#
#implies s=(8+7+6)/2=21/2=10.5#
#implies s=10.5#
#implies s-a=10.5-8=2.5, s-b=10.5-7=3.5 and s-c=10.5-6=4.5#
#implies s-a=2.5, s-b=3.5 and s-c=4.5#
#implies Delta=sqrt(10.5*2.5*3.5*4.5)=sqrt413.4375=20.333#
#implies R=20.333/10.5=1.9364# units
Hence, the radius of inscribed circle of the triangle is #1.9364# units long.
