Question

if you have the triangle ABC with the points A(47,100) B(-1273,203) and C(971,-732) how would you find the center point and the radius of the incircle of triangle ABC?

Answer 1

Wow, of the four possible centres of a triangle, the incentre is the hardest to find.
And with those awful numbers ......

by definition, it is the point which is equidistant from the 3 sides.

let the incentre be (p,q)

recall that the distance from a given point (a,b) to the line Ax + By + C = 0
is │Aa + Bb + C│ / √(A^2 + B^2)

so find the equations of each of the 3 sides, and change them to the general form Ax + By + C = 0

then form 3 different expressions for the distance to the lines, they are all equal,
so set the first equal to the second,
and the first equal to the third.

Good luck with those numbers, I certainly don't feel like doing it.