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
Tag: quadrilateral
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Cyclic quad festival
A triangle ABC with points D on AB, E on AC, and F on BC, such that ACFD and AEFB are cyclic quadrilaterals. Let DC and BE intersect at I. Show that AEID, CFIE, and BDIF are also cyclic quadrilaterals.
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Ace of diamonds II
A parallelogram is inscribed in a quadrilateral. What fraction is red?
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On all fours
Four coupled squares. Prove that the green and red quadrilateral have equal areas.
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The cheese slicer
A quarter circle of radius 1 with a yellow quadrilateral that has one side tangent to it. What is the perimeter of the quadrilateral?
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Tip of tipi
A regular hexagon is divided in four triangles and one quadrilateral. Express the hexagon area in terms of areas A, B and C.
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Bicyclic transport
EHF is tangent to the purple circle at E, and EN is tangent to the red circle at N. A and C are the circle centers. A blue rectangle has three corners HEC and the point A on one side. What is the ratio of areas, green square to orange quadrilateral?
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Quad stretches
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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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.