The amorous bugs

FOUR BUGs-A, B, C and D-occupy the corners of a square 10 inches on a side. A and C are male, Band D are female. Simultaneously A crawls directly toward B, B toward C, C toward D and D toward A. If all four bugs crawl at the same constant rate, they will describe four congruent logarithmic  spirals which meet at the center of the square. How far does each bug travel before they meet? The problem  can be solved without calculus.

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