Challenge 42: The Incenter of a Triangle

The “[b]incenter[/b]” of a triangle is the meeting point of the three angle bisectors of the angles at the triangle’s vertices. The incenter is an equal distance from the three sides of the triangle. [i]Note[/i]: The incenter of a triangle is the center of a circle inscribed in the triangle (the largest circle that fits inside the triangle. A radius of the inscribed circle is tangent to each side of the triangle, so you can construct a perpendicular from the incenter to a side to find the inscribed circle’s point of tangency – and then use this point to construct the inscribed circle.