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The chocolate muffin

Four isosceles triangles of base 1 and four of base √2 share their top vertex. What is the proportion brown : gold?

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Arc de Triomphe

A parabola passing through a square’s bottom vertices and tangent to its top side. What fraction is blue?

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The giant’s shoulder

Two equilateral triangles inside a square. What’s the proportion orange : blue?

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Buddha’s belly

A square containing a quarter circle and a tangent line segment. What is a : b?

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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 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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The life net

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

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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 pivot table

Two squares share a vertex. What is the proportion purple : green?

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Colour confinement

A semicircle with three tangent line segments. What is its area in terms of lengths a and b?