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 #(2,6)#, #(3,9)# and #(4,5)#. This will be surely distance between pair of points, which is
#a=sqrt((3-2)^2+(9-6)^2)=sqrt(1+9)=sqrt10=3.1623#
#b=sqrt((4-3)^2+(5-9)^2)=sqrt(1+16)=sqrt17=4.1231# and
#c=sqrt((4-2)^2+(5-6)^2)=sqrt(4+1)=sqrt5=2.2631#
Hence #s=1/2(3.1623+4.1231+2.2631)1/2xx9.5485=4.7742#
and #Delta=sqrt(4.7742xx(4.7742-3.1623)xx(4.7742-4.1231)xx(4.7742-2.2631)#
= #sqrt(4.7742xx1.6119xx0.6511xx2.1432)=sqrt10.7386=3.277#
And radius of inscribed circle is #3.277/4.7742=0.6864#
