Hello, RandomInquirer!

2. Is there a faster way to find out the equation of the circle inscribed in the triangle?

Example: Find the equation of the circle that is inscribed in the triangle whose sides

lie on the lines: .

The distance from a point to a line

. . is given by: .

We want a point which is equidistant from:

Substitute [4] into [5]: .

The center of the circle is: .

The radius is: .

The equation of the circle is: .