I have just baked a rectangular cake when my wife comes home and barbarically cuts out a piece for herself. The piece she cuts is rectangular, but it’s not in any convenient proportion to the rest of the cake, and its sides aren’t even parallel to the cake’s sides. I want to divide the remaining cake into two equal-sized halves with a single straight cut. How can I do it?
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A line drawn through the center of a rectangle, in any direction, will cut it evenly in two. So a line that passes through both the center of the cake and the center of the removed rectangle will divide the remaining cake into equal halves, regardless of the proportions involved or the hole’s orientation. You can find the center of each rectangle by noting the intersection of its diagonals.
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