Two circles with two common tangents. Three red lines through tangency points and centres. Prove that they are concurrent.
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Entanglement
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The parachute
A circular sector is divided as shown. What fraction is red?
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Polarisation
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
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Move the earth
A square containing a semicircle, a tangent and a line segment from the tangency point. What fraction is green?
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No pasaran
A semicircle with three tangents. The tangency points are shown. Prove that the red line segments are concurrent.
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The orange fraction
A square containing a quarter circle and a red equilateral triangle. What’s the orange fraction?
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The maxbox
A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?
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The motorcycle
Two congruent orange circles and a smaller blue one. Three common tangents are shown, one of which passes through a circle centre. What is the proportion blue : orange?
A regular hexagon, a square with its diagonals, an equilateral triangle and a circle. Prove that the hexagon and the circle are concentric.
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The triple airbag
A triangle containing three tangent semicircles with diameters a, b and c. Three line segments pass through the red tangency points. What is the triangle perimeter?