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?
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?
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 quarter circle, a semicircle and a triangle. What’s the angle α?
Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.
A quarter circle and a right triangle inside a square. One of the vertices of the triangle is the square’s centre. What fraction of the square’s area is green?