A triangle has corners at #(3 , 5 )#, #(4 ,7 )#, and #(8 ,6 )#. What is the radius of the triangle's inscribed circle?

1 Answer
Oct 9, 2017

Coordinates of incenter are (4.42, 6.09)

Explanation:

Let BC = a, AB = c, CA = b & Perimeter = p;
Let the incenter point be O.
#a=sqrt((3-4)^2+(5-7)^2)=sqrt5=2.236#
#b=sqrt((8-4)^2+(6-7)^2)=sqrt17=4.123#
#c=sqrt((8-3)^2+(6-5)^2)=sqrt26=5.099#

#p=sqrt5+sqrt17+sqrt26=2.236+4.123+5.099=11.458#

#Ox=(aAx+bBx+cCx)/p#
#Ox=((2.236*8)+(4.123*3)+(5.099*4))/11.458#
#Ox=(17.888+12.369+20.396)/11.458=# 4.421

#Oy=(aAy+bBy+cCy)/p#
#Oy=((2.236*6)+(4.123*5)+(5.099*7))/11.458#
#Oy=(13.416+20.615+35.693)/11.458=# 6.085
enter image source here