Express the x coordinate of E in terms of x coordinates of A, B, F, and G. The two black lines are supposed to be parallel to the x-axis.
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The weight lifter
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Distant sea
A rectangle with three line segments. What fraction is blue?
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Triangles galore
Four equilateral triangles. Two centres are shown. Prove that the green quadrilateral is a parallelogram.
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Encircling an anvil
Two equilateral triangles, one upside down, have boundaries meeting at 4 points, 3 of which are marked in red. Show that the circle through the red points also passes through the centre point of the blue triangle.
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Outside the pentagon
A regular pentagon and two coloured equilateral triangles. What is the angle α?
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The Swiss cheese
A triangle containing two congruent semicircles. The four tangency points are shown. What fraction is yellow?
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Bullet train
What is the ratio of orange and green areas? (The orange triangle is 45-45-90)
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Folding magic
One corner of a rectangular piece of paper is folded as shown. Prove that the red line segments are concurrent.
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Roly poly doll
Two circles with diameters (green and orange) from one of the intersection points. Show that the other intersection point of the circles is on the (purple dotted) line connecting the other ends of the diameters.
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Baby block II
A square containing another square with an extended side. What is tan(α) in terms of the red and green segment lengths?