A regular pentagon and a square share two vertices. What’s the angle α?
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The three day stubble
Month: February 2022
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It’s complicated
A circle, a semicircle and several triangles. The black points are tangency points. What proportions have the line segments a : r : b?
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The odd couple
A semicircle with two inscribed triangles The tangency points of the incircle of the bigger triangle are shown. What is the triangle area proportion orange : blue?
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Parallel universes
Two straight lines are specified by y=a+cx and y=b+cx, respectively, where b≥a. What’s the distance d between them in terms of a, b and c?
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Blazing hot
A circle inscribed in a triangle inscribed in a semicircle. The line segment through two tangency points meets a radius at the semicircle circumference. What is the angle α?
Three squares are placed as shown. What fraction of the total area is green?
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The turning point
Two isosceles triangles share a vertex. What is the maximum of their area proportion red/green?
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The kingsize bed
A rectangle with an inscribed right triangle. What is ac/bd?
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The obstructed view
A rectangle and two squares of side length a and b respectively. What is the red area in terms of a and b?
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Mickey Mouse
Three regular pentagons and two extended sides. What fraction of the total area is red?