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只用圆规作出两点的中点

By: Zhiqiang Ma On: Jan 29, 2010 Views: 9 No Comment Print Email
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只使用圆规作出给定两点的中点.

作法:
1. 以A为圆心, 半径=AB作圆1, 令AB=R.
2. 以B为圆心, 半径=R作圆2, 交圆1于C, D两点, 令CD=R’.
3. 以C为圆心, 半径=R’作圆3, 交圆1于E点, 则BE=2R为圆1的直径.
4. 以E为圆心, 半径=2R作圆4, 交圆2于G, H两点, 则BG=BH=R.
5. 以G为圆心, 半径=R作圆5.
6. 以H为圆心, 半径=R作圆6, 交圆5于I点, 则I即为A, B中点.

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