A triangle has corners at (2 , 8 ), (5 ,7 ), and (3 ,1 ). What is the radius of the triangle's inscribed circle?

1 Answer
Sep 30, 2017

midpoint of (2,8) and (5,7) = (3.5,7.5)
slope of line between (2,8) and (5,7) = (8-7)/(2-5) = -1/3
:. slope of perpendicular line = - 1/(-1/3) = 3
point slope equation:
y-7.5 = 3(x-3.5)
y = 3x-10.5+7.5
y = 3x-3

midpoint of (2,8) and (3,1) = (2.5,4.5)
slope of line between (2,8) and (3,1) = (8-1)/(2-3) = -7
:. slope of perpendicular line = - 1/(-7) = 1/7
point slope equation:
y-4.5= 1/7(x-2.5)
y = 1/7x-5/14+4.5
y = 1/7x-34/7

Now we get the system of equations:
y = 3x-3
y = 1/7x-34/7

Solving, we get (-13/20,-99/20)

The distance between (-13/20,-99/20) and (3,1) gives the radius of the circle.

=sqrt(19490)/40 ~~ 6.98