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=7, b=7 and c=6#
#implies s=(7+7+6)/2=20/2=10#
#implies s=10#
#implies s-a=10-7=3, s-b=10-7=3 and s-c=10-6=4#
#implies s-a=3, s-b=3 and s-c=4#
#implies Delta=sqrt(10*3*3*4)=sqrt360=18.9736#
#implies R=18.9736/10=1.89736# units
Hence, the radius of inscribed circle of the triangle is #1.89736# units long.
