Halving the Perimeter of a Zigzag Polygon
A a closed zigzag polygon is made from two isosceles triangles with base 1 and altitude , and a similar triangle with base 2. A straight line through the origin and inclined at an angle cuts the polygon into two parts. What is the length of the blue part?
Let be the intersection of the lines and . The triangle is congruent to the triangle , and the line cuts the rhombus in half.