A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.
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The square of Amaresh
Tag: quadrilateral
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The French kiss
Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?
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Similar intention
A cyclic quadrilateral and two diagonals. What fraction of its area is blue?
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Z
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
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The flying saucer
A quarter circle with four chords. What is the proportion purple : gold?
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The freight elevator
Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.
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Brothers in arms
The tangency points of two tangents of a circle are connected. Three perpendiculars are drawn from a point on the circle, of which two have a given length. What’s the proportion red : yellow?
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The tornado
A quadrilateral covers exactly half of the area of a rectangle. Find the length x in terms of a, b and c.
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The tipping point
Two touching circles, two diameters and two common tangents. What is the area of the green quadrilateral in terms of radii x and y?
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Square eyes
A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?