A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.
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The inner parallel
Month: November 2022
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Letting go
Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?
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Orange above
A square contains a right triangle. What fraction is orange?
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The double flag
Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?
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The door stop
A triangle with a cevian. What is α?
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Four to twelve
A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?
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The japanese progression
An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?
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The triangular tiling
A rectangle is divided into four similar triangles. What fraction is blue?
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The righteous four
Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?
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The gyroscope
Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.