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Beginner

Orange above

A square contains a right triangle. What fraction is orange?

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Intermediate

The double flag

Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?

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Advanced

The door stop

A triangle with a cevian. What is α?

Categories
Beginner

Four to twelve

A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?

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Intermediate

The japanese progression

An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?

Categories
Beginner

The triangular tiling

A rectangle is divided into four similar triangles. What fraction is blue?

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Intermediate

The righteous four

Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?

Categories
Intermediate

The gyroscope

Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.

Categories
Intermediate

The mahogany triangle

A square contains an isosceles triangle with an extended altitude. What fraction is mahogany?

Categories
Intermediate

Eight corners

A regular octagon with two diagonals and two squares. What’s the area proportion of the blue to the red square?