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The inner parallel

A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.

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The door stop

A triangle with a cevian. What is α?

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The oppressed minority

A square with two inscribed squares. What is the maximal proportion green : blue?

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Cherry picking

Two quarter circles and a red circle tangent to two chords. What fraction is red?

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Entanglement

Two circles with two common tangents. Three red lines through tangency points and centres. Prove that they are concurrent.

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The maxbox

A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?

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The grazing shot

A parabola and its directrix in red. Two tangents intersect at a point on the directrix. What’s the angle α?

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The bell tolls

An equilateral triangle inscribed in a rectangle. What is its area X in terms of triangle areas A and B?

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The new moon

A circle with two tangents, two chords and a secant. Prove that red and green are parallel.

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Slightly skewed

Two overlapping equilateral triangles with side lengths 1. What is the total red length?