The punctured hexagon
A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.
Video: Balancing Act II
Circle triplet
Identical circles have their centers aligned as shown, with the middle circle inscribed in a triangle. Show that the outer circles can be made tangent to the green circumcircle if the red axis is rotated correctly.
Wedge the wedge
An equilateral triangle containing an isosceles triangle that is not equilateral. What’s the angle α?
Video: Mind the steps
Blowing bubbles
Three congruent blue circles with a common intersection point. Prove that the red circle through the other intersections is also congruent.
Vanishing point II
Six squares and four coloured triangles. What is red : blue : yellow : green?
Video: In and out
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.