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Hint to puzzle 77: Minimal straight cut

Considering the diagram below:

Find the value of xy.
Express z in terms of x and y
Hence find the minimum value of z.

Similarly, consider a bisector from AB to BC.

Isosceles right triangle with sides AB=1, BC=1, AC=square root of 2. Let X lie on AB with AX=x, and Y lie on AC with AY=y. Then XY is a straight cut, of length z.