A square and an equilateral triangle are divided in several polygons. What is the proportion yellow : blue?
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The root cause
Month: February 2022
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Round and pointy
A circle is inscribed in both a semicircle and a right triangle. The three tangency points are shown. What is the angle α?
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The emerging pattern
A square, a circle and its centre. Prove that the six red points are on one circle.
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And counting
A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?
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The holy number
An equilateral triangle and several line segments. What fraction is purple?
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Protection
Two coloured squares inside a triangle inside a square of side length a. What is the length proportion a : b?
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Elasticity
Four squares and two triangles. Prove that the two green angles are congruent.
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The miniature version
Two rectangles share a vertex. Two line segments connecting opposing vertices and the common side intersect in a single point. Prove that the rectangles are similar.
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Wheels in motion
Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.
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The Transamerica Pyramid
Two squares inscribed in a triangle. What fraction of its area is coloured?