A semicircle and two tangent circles (tangency point shown). What is the angle α?
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The cheese dome
Month: June 2023
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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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Rolling level
Blue and green circles with tangents. The green tangent line goes through the blue tangent point and the points IJH are collinear. Show that the blue and orange lines are parallel.
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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?
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The Cheshire Cat grin
What is the total area of the green teeth relative to the large circle area? (Assume the inner circle radius is 80% of the outer. The 32 lines forming the tooth sides are concurrent, and spaced at equal angles apart.)
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The high-water mark
Two equilateral triangles on a blue line segment. Prove that the red line segment is parallel to it.
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The crown II
Several triangles and three congruent angles. Prove that the red point is the incentre of the yellow triangle.
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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 camping
A square containing an isosceles triangle. What’s the angle α?