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Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral?

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## The colour purple

A rectangle is split by two perpendicular lines. The four circles pass through vertices and intersection points. Their centres form a purple quadrilateral. What fraction of the large rectangle area does it cover?

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## The stained glass

Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?

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## The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

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## The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

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## The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

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## Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

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## The bigger picture

In a small square two perpendicular lines are drawn. A larger parallel square is constructed as shown. Prove it is a scaled copy of the smaller square but rotated 90° anticlockwise.

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