A regular pentagon and a square share two vertices. What’s the angle α?
Month: February 2022
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?
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?
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?
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?
The turning point
Two isosceles triangles share a vertex. What is the maximum of their area proportion red/green?
The kingsize bed
A rectangle with an inscribed right triangle. What is ac/bd?
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?
Mickey Mouse
Three regular pentagons and two extended sides. What fraction of the total area is red?