在Rt三角形ABC中,∠ACB=90°,CA=CB,有一个圆心角为45°,半径的长等于CA的扇形CEF绕点C旋转且直线CE、CF分别于直线AB交于点M、N当扇形CEF绕点C在∠ACB的内部旋转时,求证MN²=AM²+BN²
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![在Rt三角形ABC中,∠ACB=90°,CA=CB,有一个圆心角为45°,半径的长等于CA的扇形CEF绕点C旋转且直线CE、CF分别于直线AB交于点M、N当扇形CEF绕点C在∠ACB的内部旋转时,求证MN²=AM²+BN²](/uploads/image/z/969358-22-8.jpg?t=%E5%9C%A8Rt%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2C%E2%88%A0ACB%3D90%C2%B0%2CCA%3DCB%2C%E6%9C%89%E4%B8%80%E4%B8%AA%E5%9C%86%E5%BF%83%E8%A7%92%E4%B8%BA45%C2%B0%2C%E5%8D%8A%E5%BE%84%E7%9A%84%E9%95%BF%E7%AD%89%E4%BA%8ECA%E7%9A%84%E6%89%87%E5%BD%A2CEF%E7%BB%95%E7%82%B9C%E6%97%8B%E8%BD%AC%E4%B8%94%E7%9B%B4%E7%BA%BFCE%E3%80%81CF%E5%88%86%E5%88%AB%E4%BA%8E%E7%9B%B4%E7%BA%BFAB%E4%BA%A4%E4%BA%8E%E7%82%B9M%E3%80%81N%E5%BD%93%E6%89%87%E5%BD%A2CEF%E7%BB%95%E7%82%B9C%E5%9C%A8%E2%88%A0ACB%E7%9A%84%E5%86%85%E9%83%A8%E6%97%8B%E8%BD%AC%E6%97%B6%2C%E6%B1%82%E8%AF%81MN%26sup2%3B%3DAM%26sup2%3B%2BBN%26sup2%3B)
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