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)?
Two congruent equilateral triangles and two squares. What’s the angle α?
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?
Three squares share four vertices. What is the proportion of the line segment lengths a and b?