Two rectangles inside an equilateral triangle. What fraction is red?
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The pyramid chambres
Month: March 2025
Show that the red-blue line is perpendicular to the base line.
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As within
A square with four circular sectors. The sector centres are shown in black. Prove that the three coloured triangles are congruent.
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On the ball
Five tangent circles and a chord. What is the area X of the red ball?
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Wreath
A wreath is constructed from numerous pieces regular 10-gons, leaving the red section in the middle. What is the ratio red : green.
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Ice cube III
Two squares and an extended side. What’s the angle α?
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Centres align
Two angle bisectors and an exterior angle bisector for ABC form a second triangle DHE. Green perpendicular lines from E to AC and D to AB meet at I. J is the circumcenter of ABC. How are H, J, and I related?
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Fair and square II
Three squares and two diagonals. What is orange : blue?
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Opposing sides
An equilateral triangle with a circle and two squares, one of which has an extended side. What is purple : green?
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Lights among the trees
Three green congruent triangles, with dotted lines connecting their pairwise intersections with altitude ends on the opposite sides. Show that the dotted lines are concurrent.