A circle with its centre in the origin is cut by two parallel lines that are a distance d apart. One line is passing through the leftmost and one through the lowest point of the circle. What is the area of the green trapezium in terms of d?
Three similar triangles are placed such that they form a large triangle. What is the proportion of line segments a : b?
A semicircle inscribed in a triangle inscribed in a semicircle. What fraction of the total area is blue?
A circle with three tangents and two squares. The accentuated vertex is a tangency point. What’s the angle α?
A quarter circle inside a square divides a line segment in parts of length 4 and 6. What is the square’s area?
A semicircle with three tangent line segments. What is its area in terms of lengths a and b?
Two equilateral triangles share a vertex and have their bases on the same line. A third equilateral triangle is constructed from their apexes. Prove that its apex is also on that line.
A circle touching a semicircle and a triangle. What is the proportion blue : green?
A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?
A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?