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
Intermediate

Triple dice

An equilateral triangle with three congruent squares. What’s the angle α?

Categories
Intermediate

Paper hat II

Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?

Categories
Intermediate

En garde

An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?

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Intermediate

Distant peaks

Two isosceles triangles and a right angle. What is the proportion green : gold?

Categories
Intermediate

The Lion King II

A regular hexagon and three squares. What is the proportion yellow : brown?

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
Intermediate

Warning triangle II

A square, a triangle and two equal angles. What is the angle α?

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?