A triangle with two altitudes and a circle centred in their intersection. Prove that the red line segments are parallel.
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The marble track
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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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Video: The star shaft
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Bottoming out II
A semicircle with three squares. What’s the angle α?
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The mid-circle
A blue right triangle has an orange-dotted circumcircle and a green incircle of radius 7. What is the radius of the purple circle, which is internally tangent to the orange circle and to the two sides of the right angle?
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Video: A golden year
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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 open roof
A regular hexagon with two line segments at right angles. What is the minimum of yellow : red?
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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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The star shaft
A square with an equilateral triangle. M is the triangle side midpoint. What is yellow : red?