Start with a blue triangle, and form the green triangle whose vertices bisect each circular arc connecting blue vertices. Similarly, make the red triangle from the green, and the orange triangle from the red. Prove the triangle becomes equilateral in the limit.
Two points are on opposite sides of a channel. A skew bridge, which has a fixed direction (for instance North East), can be placed anywhere along the channel. Where to place it such that the path from A to B over the bridge is the shortest?
Two squares and two line segments. If the angle α is maximal, what is yellow : red?
A square and two congruent circles with three common tangents. What’s yellow : red?
A square containing three smaller squares and a quarter circle. What fraction is orange?
Two prisoners are chained to the walls of a triangular cell. The base is covered with a mirror and a perpendicular wall is separating them. They can each see the opposite corner through a hole. Proof they can see each other through another hole at the base of the perpendicular.
Note that this problem is known as the Blanchet Theorem.
A green triangle with several line segments. Prove that the red point is its orthocentre.
Three squares and two perpendicular line segments. What is red : yellow : blue?
A rectangle containing a right triangle. What’s red : blue?
A quarter circle with two chords of given length. What is the area of the orange quadrilateral?
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