A rectangle and a square with an extended side. Prove that their areas are equal.
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Equal partition
Tag: proportion
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Crossing straps
Every side of a quadrilateral is divided into three equal parts. What is purple : orange?
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Crossing lengths
A cyclic quadrilateral (CDIF), where we form two segments: MK (green) with DM perp to FC and DK perp to FI; GJ (orange), with IG perp to FC and IJ perp to CD. What is the ratio MK:GJ ? What about MN:GN?
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Lunar ratios
A circle of radius r is interior-tangent to the larger yellow circle of radius R, with diameters overlapping. Express s/k in terms of r and R.
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The Simson split
A cyclic quadrilateral has side lengths a, c, j, and k. Three segments drop perpendicularly to two sides and one diagonal of the quad, forming the green and purple triangles between them. What is the ratio purple/green, in terms of a, c, j, k?
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Colour coating
A triangle and its circumcircle. What is red : blue?
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The shadow side
A triangle with sides of length a and c is divided by a cevian of length b. What is brown : yellow in terms of a, b and c?
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Compromise point
The angles ABD and CBD’ are equal. A circle with diameter BD intersects AB and BC at F and H. Show red = blue (FJ = HJ) when J is the midpoint of DD’.
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The cheese flag
Two squares, one of which has an extended side. What is orange : purple?
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The unfolding
Three equilateral triangles enclose three interior triangles that share a common angle size α. The outer triangles have areas s1, s2, and s3, the inner have areas t1, t2, t3. Express the ratio t1: t2: t3 in terms of s1, s2, s3.