A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?
A triangle containing a semicircle and an equilateral triangle. What fraction is golden?
A semicircle is inscribed in a rectangle. What is the minimal covered fraction?
Two congruent rectangles and squares. Proof that the four points are on one circle.
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?
An equilateral triangle with an altitude. Two of its sides form the radii of the circular sector. What fraction of the area is covered by the red circle?
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?
Two tangent circles and a triangle. The figure has reflection symmetry in the vertical diameter d, of which one ninth is above the horizontal chord. What fraction is pink?
A triangle containing two tangent semicircles. What’s the proportion α : β?