A triangle has its sides on the lines $x+2y-5=0, 2x-y-10=0$ and $2x+y+2=0$. Find the radius of the circle inscribed in the triangle.

Question

I already found the solution which is enter image description here

enter image description here

However, I am still quite confused on how we got this: enter image description here

Can someone please explain? Thank you!

Answer 1

I would graph this, find the coordinates of the vertices, calculate the length of each side using the distance formula, then calculate the perimeter and semiperimeter $s$. The area of the triangle is $sr_i$, where $r_i$ is the inradius.