几何竞赛题三角形ABC,圆S过点B并切三角形AC边于点A,圆T过点C并切三角形AB边于点A,S和T相交于点D和点A,AD所在直线交圆ABC与点E,试证AE=2AD.
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![几何竞赛题三角形ABC,圆S过点B并切三角形AC边于点A,圆T过点C并切三角形AB边于点A,S和T相交于点D和点A,AD所在直线交圆ABC与点E,试证AE=2AD.](/uploads/image/z/15223985-17-5.jpg?t=%E5%87%A0%E4%BD%95%E7%AB%9E%E8%B5%9B%E9%A2%98%E4%B8%89%E8%A7%92%E5%BD%A2ABC%2C%E5%9C%86S%E8%BF%87%E7%82%B9B%E5%B9%B6%E5%88%87%E4%B8%89%E8%A7%92%E5%BD%A2AC%E8%BE%B9%E4%BA%8E%E7%82%B9A%2C%E5%9C%86T%E8%BF%87%E7%82%B9C%E5%B9%B6%E5%88%87%E4%B8%89%E8%A7%92%E5%BD%A2AB%E8%BE%B9%E4%BA%8E%E7%82%B9A%2CS%E5%92%8CT%E7%9B%B8%E4%BA%A4%E4%BA%8E%E7%82%B9D%E5%92%8C%E7%82%B9A%2CAD%E6%89%80%E5%9C%A8%E7%9B%B4%E7%BA%BF%E4%BA%A4%E5%9C%86ABC%E4%B8%8E%E7%82%B9E%2C%E8%AF%95%E8%AF%81AE%3D2AD.)
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