Balance

balance puzzle

Point P lies within acute angle XOY. How can we find a point A on OX and a point B on OY such that P is the midpoint of a segment drawn between them?

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Draw OP and continue the line to Q so that OP = PQ. Then draw QA parallel to OY and QB parallel to OX, as shown. OAQB is a parallelogram, so its diagonals bisect one another, and thus P is the midpoint of AB. From Paul Sloane and Des MacHale’s Mathematical Lateral Thinking Puzzles, 2015.