Show equality of the green and orange square playing field areas.
Tag: square
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.
Vanishing point II
Six squares and four coloured triangles. What is red : blue : yellow : green?
Balancing act II
Two squares share a vertex. What’s the angle α?
Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)
Pop you bubble
A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.
The ceiling lamp
A regular octagon with two diagonals and a square. Prove that the four red points are concyclic.
Stay centred
Two squares share a vertex. Prove that the red point is the circumcentre of the red triangle.
Peeping out II
A unit square and a rectangle touching three square sides and passing through the midpoint of the upper side. What is the minimal blue area?
Peeping out
A unit square and a rectangle. What is the blue area?