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Premium

Video: The punctured hexagon

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Intermediate

The doubleganger

Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.

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Premium

Video: Wedge the wedge

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Advanced

The hippodrome shadow

The racer at A is running counter-clockwise around the inside of the outer purple circle, with a “shadow racer” B following behind, related by the three chords that are tangent to the inner orange circle. Does the shadow B ever catch up with A?

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Intermediate

Cherries

Two tangent circles and two green tangents. The three tangency points are shown in black. Prove that the blue line segment is a common tangent.

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Video: Blowing bubbles

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Intermediate

Sticky corners

Two equilateral triangles and several line segments. What is red : yellow?

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Intermediate

Median between sides

A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)

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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.