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Square eyes

A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?

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The Queen’s chamber

A right triangle with three squares forming a smaller inner triangle. What is the maximal blue fraction?

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The outsider

A circle with an inscribed regular pentagon, a square and a triangle. Prove that the point lies on the circumference of the circle.

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Black hole sun

A square containing two quarter circles and a common tangent. What is the proportion yellow : black?

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My two cents

A right triangle is divided in two triangles, one of which is isosceles. The two inscribed circles are congruent. What is the total area?

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The life net

The vertices of a regular hexagon are connected to midpoints of opposing sides. What fraction is red?

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The lunar twins

Three circles are tangent to each other. The black chords go through their tangency points. Prove that the red chord is a diameter of the largest circle.

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Below the line

Two squares share a vertex at the origin and have their sides along the x- and y-axis. Two vertices lie on the line satisfying x+2y=c. What is the proportion purple : yellow?

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The red planet

A semicircle with a chord and a line segment perpendicular to it. What is the total area in terms of lengths a and b?

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The ocean view

Two squares of variable size share a vertex. What is the maximal blue fraction?