Categories
Intermediate

The pleasure dome

A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?

Categories
Intermediate

Pyramidion

A triangle containing a semicircle and an equilateral triangle. What fraction is golden?

Categories
Advanced

The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

Categories
Beginner

The wall

Two congruent rectangles and squares. Proof that the four points are on one circle.

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Advanced

The satellite

A circle containing three squares. What fraction is coloured?

Categories
Advanced

The eye mask

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?

Categories
Intermediate

The red balloon

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?

Categories
Advanced

The green quad

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?

Categories
Intermediate

The strawberry ice cream

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?

Categories
Beginner

Seventies tipi II

A triangle containing two tangent semicircles. What’s the proportion α : β?