Two equilateral triangles on a line. Prove that the blue triangle is equilateral as well.
Family constellation
![Family constellation](https://mirangu.com/wp-content/uploads/2024/07/FamilyConstellation.jpg)
Two equilateral triangles on a line. Prove that the blue triangle is equilateral as well.
Two regular pentagons share a vertex. What’s the angle α?
Four coloured rectangles and three line segments. Prove that the three line segments are concurrent.
Two triangles and one incircle with its centre and tangency points. Prove that the triangles are similar.
Two squares sharing a vertex and two overlapping coloured quadrilaterals from square side midpoints. What is the area proportion of the blue and the red quadrilateral?
A cathedral is erected on two hills, the side circular arcs whose centers are the hill ends, and so that the right (and left) side arcs are orthogonal. Show that the tip of the spire is directly above where the hills meet.
Tangent lines QC and EC meet at C. A point D on QC has DC=1 and QD=2. The line ED intersects the circle at G, and the line HGI is parallel to QDC. What is HG/GI?
A semicircle and a square with extended side and diagonal. Prove that the red line segment is tangent to the semicircle.
What is the area of a green quadrilateral that fits inside a quarter circle, and has perpendicular diagonals?
Two regular pentagons sharing a vertex with extended sides and diagonals. Proof that the three red points are collinear.