Multicoloured pentangle in a red circle. Rhombuses form two levels of petals growing outward, forming a decagon. Show that the opposite sides of the two interleaved pentagons are equal in pairs and also equal and parallel to the sides of the pentangle.
A present fits inside a circle, and we tape the orange ribbons to the green midpoints of the sides, choosing them perpendicular to the opposite sides at the purple points. Show that the four ribbons have a point in common.
Four Pac-Men eat the corners of a square while four others stand guard. What fraction of the square is eaten?
Two intersecting circles with a triangle connecting them. Show that the three red points are collinear.
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.
25 darts land inside a regular-hexagonal dart board with edge length the square root of 3. Show that at least five of the darts land inside the same unit circle.
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 semicircle and two tangent circles (tangency point shown). What is the angle α?
What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.