Two squares share a vertex. Each square contains a coloured rectangle with extended side. What’s green : blue? By Matthew Arcus.
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No laughing matter
Month: March 2024
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Video: Sticky corners
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Unring a bell
A square and an equilateral triangle. What’s the angle α?
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Playing fields
Show equality of the green and orange square playing field areas.
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Video: The punctured hexagon
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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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Video: Wedge the wedge
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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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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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