A regular hexagon and an equilateral triangle share a vertex. What is red : blue?
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The see-through triangle
Tag: length
A triangle with two line segments. What’s the angle α?
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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Corner pursuit
Four corners of a square pursue each other clockwise, and after each unit step mark out the new smaller square. Show that the squares sizes in the sequence decrease in size to 1 in the limit.
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The mirror dome
A ray of light is emitted from a point on the wall of a mirror-covered semicircle and reflects four times as shown to return to the same spot. If the radius is 1, what is the length of the path?
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Half right
A right triangle with two angle bisectors. What is red : blue?
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Criss-crossing the bay
A boatsman races to cross Isosceles Bay five times, finishing at End. A bicyclist pedals around the bay. How many times faster must the bicyclist travel in order to be sure to beat the boat to End?
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The green diamond
Two equilateral triangles are placed side by side. The common (blue) side is extended. What is red : blue?
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Centre of attraction
An equilateral triangle with two perpendiculars to a point that is at the same height as the triangle centre. What is red : yellow?