A circle and several triangles. Prove that the green triangle is isosceles.
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The silly walk
Tag: angle
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The sun hat
Two triangles share a circumcircle and vertex, with one edge of the orange triangle containing the feet of two of the altitudes of the blue triangle. Show that the orange triangle is isosceles.
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Uneasy the head
The green zigzag crown segments would extend through either B or C. Show that the arcs along the top are equally spaced.
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Falling in
Start with an acute triangle and form a new triangle from the points of tangency of its inscribed circle. Continue this process to make make the triangle with blue vertices. What is the maximum possible angle at a blue vertex?
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Smugglers
The smugglers want to land half-way between the lighthouses. It is a dark night, so they keep their boat heading at an angle bisecting the angle to the two lights. Where on the shore should the coast guard wait to intercept them?
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Bottoming out II
A semicircle with three squares. What’s the angle α?
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Between the lines II
Two rectangles are at right angles and have equal area. Prove that the three black lines are parallel.
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The heptagon square
What is the angle α between the blue line and the baseline of the orange square?
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Needles and yarn
The purple yarn is stretched between the coloured needles approximately as shown, and the yarn is repositioned to make the shortest path of that type. What is the length ratio purple/green?
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Inside the box
Two squares inside a square share a vertex. What’s the angle α?