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## 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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## The bear trap

A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?

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What is the area of the trapezium in terms of lengths a and b?

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## Harmonic proportions

A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.

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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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## The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

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## Parallelism

A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?

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## Pulling the strings

Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.

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