The Nine-Part Triangle

Strategies and Hints

  1. The left leg is subdivided into 3 equal parts.

  2. The diameter of the circle equals the top leg. Divide the diameter into 3 equal parts. Then draw perpendicular line segments up to meet the circle. Two more line segments connect these intersections with the right vertex of the original triangle.

  3. The intersections of the 2 large circles with the diameter of the smallest circle provide the points needed to mark off the top leg of the triangle.

Solution

The complete construction for the original problem is shown here.