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Advanced

Through the roof

A semicircle with its centre. What is green : red in terms of the angles α and β?

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Intermediate

Airbag ball

A triangle with its excircles. The tangent radii are extended. Prove that the red line segments are concurrent and congruent.

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Beginner

Folding a pentagon

One side of a regular pentagon is folded back and forth as shown. Are the six red line segments congruent?

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Intermediate

Snow man scarf

Show that blue = red if and only if purple = orange.

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Beginner

Lemon slice II

A semicircle inscribed in a quarter circle. What fraction is yellow?

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Advanced

Cuckoo in the nest

Two tangent semicircles inscribed in another semicircle. What is the total area?