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The inner parallel

A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.

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Intermediate

Letting go

Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?

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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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The door stop

A triangle with a cevian. What is α?

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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?

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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?

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Intermediate

The gyroscope

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