A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.
Category: Beginner
Two-story A-frame house
The slanted lines are perpendicular, and the one in the bottom story bisects the angle. Show that red equals green, so the stories have the same height.
Angle versus height
What is the ratio orange/green?
The Bedouin tent
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?
A red equilateral triangle and its circumcircle. Prove that the blue triangle is also equilateral.
Domino day II
Two large congruent rectangles share a vertex and contain two coloured rectangles. What is red : blue?
Stay centred
Two squares share a vertex. Prove that the red point is the circumcentre of the red triangle.
Peeping out
A unit square and a rectangle. What is the blue area?
Pythagoras times three
Three squares on a grid. What is the ratio of the areas red : green : purple?
Bandaged head
A regular decagon and triangles from vertices and side midpoints. What fraction is red?