Two triangles and one incircle with its centre and tangency points. Prove that the triangles are similar.
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Ten to nine
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Video: Square mouse
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Quad stretches
Two squares sharing a vertex and two overlapping coloured quadrilaterals from square side midpoints. What is the area proportion of the blue and the red quadrilateral?
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Cathedral on the hills
A cathedral is erected on two hills, the side circular arcs whose centers are the hill ends, and so that the right (and left) side arcs are orthogonal. Show that the tip of the spire is directly above where the hills meet.
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Video: Triangulation
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A devious cevian
A triangle with a cevian. It is split into two similar triangles. What is angle ABC?
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Video: Ice cream cone II
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Ends of the spectrum
Two squares and a rectangle. Prove that red = blue.
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Tangent latitudes
Tangent lines QC and EC meet at C. A point D on QC has DC=1 and QD=2. The line ED intersects the circle at G, and the line HGI is parallel to QDC. What is HG/GI?
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