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: quadrilateral
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Touch the sides
What is the area of a green quadrilateral that fits inside a quarter circle, and has perpendicular diagonals?
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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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Spotlight II
A square is divided in several triangles and quadrilaterals. What is yellow : red?
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The square sail
A quadrilateral and a parallelogram share two sides, and a vertex from each determine the orange square. The lengths BC, EF, AD are 4,5,7 respectively, where E and F are midpoints of AB and DC. What is the orange area?
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Eclipsing earth
Two circles with their centres. The quadrilateral ABCD is cyclic and has two sides tangent to the small circle. Prove that BD is also tangent.
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Dancing squares
Four squares and one centre. Prove that the red quadrilateral is a parallelogram.
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Triangles galore
Four equilateral triangles. Two centres are shown. Prove that the green quadrilateral is a parallelogram.
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The same vein
Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.
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The boomerang
A quadrilateral and a triangle. What’s the angle α?