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Beginner

Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

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Beginner

Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

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Beginner

Square offspring

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

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Beginner

Triangle offspring

Four equilateral triangles. Prove that the three black line segments are concurrent.

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Beginner

The punctured hexagon

A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.

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Beginner

Two-story A-frame house

The slanted lines are perpendicular, and the one in the bottom story bisects the angle. Show that red equals green, so the stories have the same height.

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Beginner

Angle versus height

What is the ratio orange/green?

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Beginner

The Bedouin tent

A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?

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Beginner

Hats off

A red equilateral triangle and its circumcircle. Prove that the blue triangle is also equilateral.

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Beginner

Domino day II

Two large congruent rectangles share a vertex and contain two coloured rectangles. What is red : blue?