Categories
Beginner

Colour confinement

A semicircle with three tangent line segments. What is its area in terms of lengths a and b?

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Intermediate

Two steps forward

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.

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Advanced

The earth projection

A circle touching a semicircle and a triangle. What is the proportion blue : green?

Categories
Intermediate

Crazy frog

A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?

Categories
Beginner

Composition in red, blue and yellow

A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?

Categories
Beginner

The dark lord

Two congruent equilateral triangles and two squares. What’s the angle α?

Categories
Intermediate

The pointy shoe

A quarter circle, a semicircle and a triangle. What’s the angle α?

Categories
Advanced

Cordon sanitaire

Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.

Categories
Intermediate

The green zone

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?

Categories
Beginner

The open book

Three squares share four vertices. What is the proportion of the line segment lengths a and b?