Challenge 42: The Incenter of a Triangle
- Gerry Stahl
The “incenter” 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. Note: 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.