A triangle with three line segments to an internal point. What’s the angle α?
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Missing an angle
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Seven chords
A regular 7-gon inscribed in a circle (ABCDEFG), with some other point H on the circle, in the arc CD. Show that the length sum of the blue chords equals the length sum of the green chords.
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The two-state solution
Two congruent squares share a vertex. What fraction is yellow?
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Wild floor tile
What is the ratio of areas, purple/green, when the orange octagon is regular (all angles equal)?
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Euclid’s wing
Several line segments, some of which are parallel. What is green : orange?
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The mirror box
Light rays bounce off mirrored walls of a square before reaching one of the other corners. What are the slopes of the light rays leaving A that land in one of the corners B or D after exactly k=5 reflections?
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Dancing squares
Four squares and one centre. Prove that the red quadrilateral is a parallelogram.
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Making a dent
A right triangle with one trisected angle. What’s the angle α?
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Mix master
What is the sum of the angles at the blue vertices of this 11-gon?
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A central angle
One blue and two congruent red squares. The shown point is the red square centre. What is the angle α?