A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?
Month: July 2021
Five unit squares inside a larger square. What is the total area?
The axe head
A tetrahedron with given vertex coordinates. What is its volume?
The sleeping bag
A semicircle containing a circle. One line segment is tangent to the circle and connects to the semicircle centre. The chord connects two tangency points. What fraction is blue?
A full house
Two large squares and three smaller ones of side length 5 are placed as shown. What is the pink area?
The stained glass
Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?
Tilted hourglass II
Two equilateral triangles inside a square. What’s the proportion green : orange?
The hot-air balloon
Two circles, four tangent line segments and a square. What’s the proportion red : blue?
The crazy diamond
Three rectangles and four triangles. Given that the red triangles have equal area, prove that the blue rectangles are similar.
Partial eclipse II
Two diagonals of a circle are tangent to another circle. The chord passes through the tangency point. If the smaller circle has area 3, what is the area of the larger one?