The blue quadrilateral contains a purple interior point which is a corner for two right angles. Reflect the purple point about the four sides of the quadrilateral. Show that the four image points are concyclic.
A unit square and a point on the inscribed circle. What is a2+b2+c2+d2?
Three congruent squares share two vertices while the upper sides coincide. What’s red : blue?
The symmetrical figure bounded by 4 black semicircles is what Archimedes called the “salinon” or “salt cellar”. Show it has the same area as the green disc of the same height.
Three congruent rectangles on a line. Prove that the four red points are cyclic.
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.
Three congruent rectangles on a line. What’s the angle α?
Express the area of the orange triangle in terms of the areas of the other colours.
A regular hexagon and an equilateral triangle share a vertex. What is red : blue?
A square, two orthogonal axes and two angles. What’s the proportion α : β?