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## Fair and square

Two squares of which three vertices form an isosceles triangle. What is the angle α?

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## The golf ball

A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.

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## Égalité

A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?

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## The bungee cords

Three squares and two line segments. What’s the angle α?

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## The pentagon attack

Two regular pentagons and two diagonals. What’s the angle α?

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## Lean on me

Two squares and two diagonals. Prove that the angles α and β are equal.

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## Twin balls

A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?

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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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