Question

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

Answer 1

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