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Halving the Perimeter of a Zigzag Polygon

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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?

Contributed by: Izidor Hafner (October 2013)
Open content licensed under CC BY-NC-SA

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Let be the intersection of the lines and . The triangle is congruent to the triangle , and the line cuts the rhombus in half.

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