Two squares sharing a vertex and two overlapping coloured quadrilaterals from square side midpoints. What is the area proportion of the blue and the red quadrilateral?
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Quad stretches
Tag: square
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Ends of the spectrum
Two squares and a rectangle. Prove that red = blue.
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Square mouse
A semicircle and a square with extended side and diagonal. Prove that the red line segment is tangent to the semicircle.
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Triangulation
A regular dodecagon contains a yellow square. Find the three angles α, β and γ.
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Paranoid centroid
A square is divided in four triangles of which the red centroids are shown. What fraction is green?
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Blocking the view
Two squares and one extended side. What is purple : red?
A square with two semicircles. The smaller one has an extended diameter and a tangent. What are the coordinates of the tangency point?
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Squaring the quad
Form inward semicircles (orange) and outward semicircles (purple) on two opposite sides of a quadrilateral. Connect the midpoints of the orange arcs, intersecting with the purple arcs. Show that you obtain two corners of an enclosing square.
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Wheel in motion
A circle with its centre and two squares sharing a vertex. What’s the angle α?
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Square construction
Given the blue square AEFI and a point B inside, show that the intersection H of the red and purple semicircles will be a corner of a square containing B on one side and A on another, and sharing the corner I with the blue square.