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Video: Vanishing point II

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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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Video: Balancing Act II

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Advanced

Circle triplet

Identical circles have their centers aligned as shown, with the middle circle inscribed in a triangle. Show that the outer circles can be made tangent to the green circumcircle if the red axis is rotated correctly.

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Intermediate

Wedge the wedge

An equilateral triangle containing an isosceles triangle that is not equilateral. What’s the angle α?

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Video: Mind the steps

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Intermediate

Blowing bubbles

Three congruent blue circles with a common intersection point. Prove that the red circle through the other intersections is also congruent.

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Intermediate

Vanishing point II

Six squares and four coloured triangles. What is red : blue : yellow : green?

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Video: In and out

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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.