AB、CD为圆O的两条弦,M、N分别为AB、CD的中点,且角AMN=角CNM,求证AB=CD证明:如图,连接OM,ON∵M、N分别为AB、CD的中点∴OM⊥AB,ON⊥CD∴∠CNO = ∠AMO = 90°∵∠AMN =∠CNM∴∠OMN=∠ONM∴OM = ON∴AB=CD 证明过
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![AB、CD为圆O的两条弦,M、N分别为AB、CD的中点,且角AMN=角CNM,求证AB=CD证明:如图,连接OM,ON∵M、N分别为AB、CD的中点∴OM⊥AB,ON⊥CD∴∠CNO = ∠AMO = 90°∵∠AMN =∠CNM∴∠OMN=∠ONM∴OM = ON∴AB=CD 证明过](/uploads/image/z/5198993-17-3.jpg?t=AB%E3%80%81CD%E4%B8%BA%E5%9C%86O%E7%9A%84%E4%B8%A4%E6%9D%A1%E5%BC%A6%2CM%E3%80%81N%E5%88%86%E5%88%AB%E4%B8%BAAB%E3%80%81CD%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E4%B8%94%E8%A7%92AMN%3D%E8%A7%92CNM%2C%E6%B1%82%E8%AF%81AB%3DCD%E8%AF%81%E6%98%8E%EF%BC%9A%E5%A6%82%E5%9B%BE%2C%E8%BF%9E%E6%8E%A5OM%2CON%E2%88%B5M%E3%80%81N%E5%88%86%E5%88%AB%E4%B8%BAAB%E3%80%81CD%E7%9A%84%E4%B8%AD%E7%82%B9%E2%88%B4OM%E2%8A%A5AB%2CON%E2%8A%A5CD%E2%88%B4%E2%88%A0CNO+%3D+%E2%88%A0AMO+%3D+90%C2%B0%E2%88%B5%E2%88%A0AMN+%3D%E2%88%A0CNM%E2%88%B4%E2%88%A0OMN%3D%E2%88%A0ONM%E2%88%B4OM+%3D+ON%E2%88%B4AB%3DCD+%E8%AF%81%E6%98%8E%E8%BF%87)
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