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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