A quarter circle with four chords. What is the proportion purple : gold?
The dance
A regular hexagon, two squares and a semicircle connecting two vertices. Is the red vertex located on the semicircle?
The hidden circle
Two intersecting circles, two line segments and five points, two of which are centres. Prove that the red points are concyclic.
Big brother
Two squares and three line segments. What’s the angle α?
Missing pieces
A rectangle is divided in six similar triangles. What is the proportion green : yellow : red : blue?
The root cause
A square and an equilateral triangle are divided in several polygons. What is the proportion yellow : blue?
Round and pointy
A circle is inscribed in both a semicircle and a right triangle. The three tangency points are shown. What is the angle α?
The emerging pattern
A square, a circle and its centre. Prove that the six red points are on one circle.
And counting
A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?
The holy number
An equilateral triangle and several line segments. What fraction is purple?