Two equilateral triangles are placed as shown. Their centres are connected as well as their intersection points. What’s the angle α?
The radical
Two intersecting circles and a common tangent. The two tangency points are shown in black. Prove that the three red points are collinear.
Getting stuck
A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?
The dirty thirties
A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?
Scratching the surface
Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?
The Moroni minimum
An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?
To the core
A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.
Family ties
Two regular pentagons share a vertex. What is the proportion red : green?
The seventh bell
A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?
Longing for spring
Four semicircles and three line segments. What’s the proportion yellow : orange?