A rectangle containing three line segments. What fraction is blue?
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Night mountain
Tag: triangle
The red and green wedges subtend the same angle, there are two right angles, and the blue sides have the same length. What is the ratio of lengths of the green and red segments?
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Downhill skiing
Choose any point D on the side AB of an isosceles triangle ABC, then extend the side AC beyond C to a point F with |CF| = |DB|. Show that the segment DF is cut exactly in two by the third side BC—that the orange and red trails are equal.
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Wrapping presents II
Six squares are placed around a triangle. What is the angle α?
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Off the grid
A square on a grid containing a red triangle with an extended side. What is the red fraction?
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Folded napkin II
A unit square paper is folded as shown. What is the red area?
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Tip the scale
Two equilateral triangles and a square. What’s the angle α?
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Hidden circle II
What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.
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Half right
A right triangle with two angle bisectors. What is red : blue?
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Your turn
A regular hexagon of which the centre is a vertex of an equilateral triangle. What is the angle α?