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## The common triangle

Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.

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## The fried egg

Two concentric circles and two tangents. What is the yellow fraction?

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## The parallax effect

Two intersecting circles with a triangle that passes through their centres and an intersection point. What’s the angle α?

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## The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

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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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## Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

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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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## The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

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