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A piece of paper in the shape of an equilateral ABC has AB = 8.  When A is folded over to any point on BC, a crease of length x is formed which joins some point of AC to some point of AB.  As A is moved along BC from B to C, x varies.  If the greatest value of x is M and the least value of x is m, find the ordered pair (M,m).

 Dec 6, 2019
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The longest crease will occur when A is folded onto B (or C), which gives a crease of length \(M=4\sqrt3\)

 

From the symmetry of the triangle the shortest crease will occur when A is centred between B and C, giving \(m=4\)

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 Dec 6, 2019
edited by Alan  Dec 6, 2019

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