A quadrilateral and an internal point from which four line segments are drawn, each parallel to a different side. What is blue : orange?
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A limited scope
Month: February 2025
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Rectangular justice
Purple and blue rectangles with line KL connecting their centers. What is the area ratio Green:Orange?
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Right angle II
A rectangle with several line segments. What’s the angle α?
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Cocked hats
Three squares and a right triangle. How are the green, orange, and blue areas related?
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Eye of Providence
A regular pentagon and an equilateral triangle. What is the angle α?
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Party mask
Touching green and blue circles are connected by an orange semicircle whose ends are C on the green circle and E, the center of the blue circle. C, A, B are collinear, and D is on both the green circle and the semicircle. Show that the circle (CDB) is tangent to the blue circle at B.
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Velocipede IV
Two circles with three common tangents. The smaller radius is extended as shown. Express the extension length x in terms of R and r.
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Egyptian sunset II
Three equilateral triangles with areas 1, x and x² fit inside a semicircle. What is x?
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Moving boxes
Five squares inside a square. Prove that the three red vertices are collinear.
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Overburdened
A fixed red circle hovers centered above a fixed segment AB, with relative dimensions as shown. Determine the quotient of areas blue/green, and show that it does not depend upon the choice of the point J on the red circle.