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## The queen

A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?

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## The leftward lean

Two triangles form a quadrilateral. What’s the total orange area?

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## We are equal

A quadrilateral with its diagonals. What’s the angle α?

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## The square of Amaresh

A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.

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## The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?

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## Similar intention

A cyclic quadrilateral and two diagonals. What fraction of its area is blue?

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## Z

A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?

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## The flying saucer

A quarter circle with four chords. What is the proportion purple : gold?

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