A semicircle containing two equilateral triangles and a circle. What’s the yellow fraction?
Month: October 2022
Five to twelve
A square and a rectangle share two vertices. If the square has twice the area of the rectangle, what’s the angle α?
Entanglement
Two circles with two common tangents. Three red lines through tangency points and centres. Prove that they are concurrent.
The parachute
A circular sector is divided as shown. What fraction is red?
Polarisation
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
Move the earth
A square containing a semicircle, a tangent and a line segment from the tangency point. What fraction is green?
No pasaran
A semicircle with three tangents. The tangency points are shown. Prove that the red line segments are concurrent.
The orange fraction
A square containing a quarter circle and a red equilateral triangle. What’s the orange fraction?
The maxbox
A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?
The motorcycle
Two congruent orange circles and a smaller blue one. Three common tangents are shown, one of which passes through a circle centre. What is the proportion blue : orange?