Maths Olympiad Prep

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UKMT Mathematical Olympiad for Girls, 2013

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows three identical overlapping right-angled triangles, made of coloured glass, placed inside an equilateral triangle, one in each corner. The total area covered twice (dark grey) is equal to the area left uncovered (white). What fraction of the area of the equilateral triangle does one glass triangle cover?

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