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Conway circular area
A triangle with sides a, b, c, when extended to whiskers of opposite side length, forms the “Conway Circle”. What is the area of the circle in terms of the expressions a+b+c, ab+bc+ca, abc of the side lengths a, b, c.
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Family constellation
Two equilateral triangles on a line. Prove that the blue triangle is equilateral as well.
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Video: Quad stretches
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Tipping point II
Two regular pentagons share a vertex. What’s the angle α?
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All connected
Four coloured rectangles and three line segments. Prove that the three line segments are concurrent.
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Video: A devious cevian
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Drilling site
A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?
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Video: Ends of the spectrum
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Rolling along
Tangents to the blue circle (ABC) intersect at a point K, and the line AK intersects (ABC) at H. D is the midpoint of BC. Show that the green circle (DHB) is tangent to the line AB.