A semicircle is inscribed in a rectangle. What is the minimal covered fraction?
A circle containing three squares. What fraction is coloured?
A right triangle with its inscribed circle. Two cevians are drawn through the circle centre. What is the circle area in terms of triangle areas A and B?
Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral?
Three coloured equilateral triangles share three vertices. Prove that the triangle formed by their centres is also equilateral.
A semicircle is inscribed in a quarter circle. What is the minimal yellow fraction?
A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?
A circle of radius r touching both sides of a parabola having focal length a. A line segment tangent to the circle is split in two equal segments of length d. What is d in terms of r and a?
The edge of a circle is folded to touch a diameter. The tangency point lies 2 from the centre. Given that the fold has length 4, what was the circle area before folding?
Two congruent circles and a right triangle inside a semicircle. What fraction is blue?