One corner of a rectangular piece of paper is folded as shown. Prove that the red line segments are concurrent.
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Folding magic
Month: September 2023
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Roly poly doll
Two circles with diameters (green and orange) from one of the intersection points. Show that the other intersection point of the circles is on the (purple dotted) line connecting the other ends of the diameters.
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Baby block II
A square containing another square with an extended side. What is tan(α) in terms of the red and green segment lengths?
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Tilted hourglass III
A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?
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Flying purple people eater
What is the area of the purple people eater, in terms of the lengths AD and BC?
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Primary colours
An equilateral triangle inside a rectangle. What is red : yellow : blue?
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Mountain roads
A circular mountain peak has coordinates (0,0,3) and its base has towns C=(-4,0,0), E=( 4,0,0) on opposite sides. Town D=(0,4,0) is halfway between them, around the base. A road goes partially up and down the mountain connecting C and E. Another road connects C and D. Both roads are shortest possible. What is the ratio of the road lengths?
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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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Mouth to mouth
What is the ratio of the blue and yellow lines?
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Equal rights
Two squares sharing a vertex. Two vertices are connected by a line segment. What is yellow : green?