If the sides of a triangle are #a#, #b# and #c#, then the area of the triangle #Delta# is given by the formula
#Delta=sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#
and radius of inscribed circle is #Delta/s#
Hence let us find the sides of triangle formed by #(2,5)#, #(4,8)# and #(4,6)#. This will be surely distance between pair of points, which is
#a=sqrt((4-2)^2+(8-5)^2)=sqrt(4+9)=sqrt13=3.6056#
#b=sqrt((4-4)^2+(6-8)^2)=sqrt(0+4)=sqrt4=2# and
#c=sqrt((4-2)^2+(6-5)^2)=sqrt(4+1)=sqrt5=2.2631#
Hence #s=1/2(3.6056+2+2.2631)=1/2xx7.8687=3.9344#
and #Delta=sqrt(3.9344xx(3.9344-3.6056)xx(3.9344-2)xx(3.9344-2.2631)#
= #sqrt(3.9344xx0.3288xx1.9344xx1.6713)=sqrt4.18226=2.045#
And radius of inscribed circle is #2.045/3.9344=0.52#
