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## The lighthouse

A parallelogram and four equilateral triangles. What is yellow : green?

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## Pink parallels

A pink parallelogram with two extended sides. What’s α : β?

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## Three’s a crowd

Four equilateral triangles. Prove that the red quadrilateral is a parallelogram.

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## The gyroscope

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

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## The beam in your eye

Three parallelograms are inscribed in a circle. Prove that the common red vertex is the orthocentre of the dashed triangle.

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## The iron curtain

A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.

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## The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

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## Out of proportion

An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?

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