Three small balloons are in congruent sheds awaiting lift off. The middle shed opens its side flaps. Show that its balloon can inflate, without rolling it, until it is tangent to the sides of the adjacent sheds.
Three squares and a circle. Prove that the red point is on two squares and the circle.
Five squares in a configuration. What’s the angle α?
Six squares are placed around a triangle. What is the angle α?
Four corners of a square pursue each other clockwise, and after each unit step mark out the new smaller square. Show that the squares sizes in the sequence decrease in size to 1 in the limit.
A ray of light is emitted from a point on the wall of a mirror-covered semicircle and reflects four times as shown to return to the same spot. If the radius is 1, what is the length of the path?
A unit square paper is folded as shown. What is the red area?
What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.
A right triangle with two angle bisectors. What is red : blue?
A regular hexagon of which the centre is a vertex of an equilateral triangle. What is the angle α?