初三数学切线的判定如图所示,△ABC是直角三角形,∠ABC=90°,以AB为直径的圆O交AC于点E,点D是BC边的中点,连结DE.(1)求证:DE与圆O相切;(2)若圆O的半径为根号3,DE=3,求AE.
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![初三数学切线的判定如图所示,△ABC是直角三角形,∠ABC=90°,以AB为直径的圆O交AC于点E,点D是BC边的中点,连结DE.(1)求证:DE与圆O相切;(2)若圆O的半径为根号3,DE=3,求AE.](/uploads/image/z/12874130-26-0.jpg?t=%E5%88%9D%E4%B8%89%E6%95%B0%E5%AD%A6%E5%88%87%E7%BA%BF%E7%9A%84%E5%88%A4%E5%AE%9A%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%2C%E2%96%B3ABC%E6%98%AF%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2%2C%E2%88%A0ABC%3D90%C2%B0%2C%E4%BB%A5AB%E4%B8%BA%E7%9B%B4%E5%BE%84%E7%9A%84%E5%9C%86O%E4%BA%A4AC%E4%BA%8E%E7%82%B9E%2C%E7%82%B9D%E6%98%AFBC%E8%BE%B9%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E8%BF%9E%E7%BB%93DE.%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9ADE%E4%B8%8E%E5%9C%86O%E7%9B%B8%E5%88%87%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5%E5%9C%86O%E7%9A%84%E5%8D%8A%E5%BE%84%E4%B8%BA%E6%A0%B9%E5%8F%B73%2CDE%3D3%2C%E6%B1%82AE.)
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