Two equilateral triangles and one centre. What’s green : red?
Author: Rik D. Tangerman
The new normal
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?