已知,三角形ABC内接于圆O,AD是圆O直径,点E、F分别在AB、AC的延长线上,EF交圆O于M、N,交AD与点H,H是OD的中点,弧MD=弧DN,EH-HF=2,设角ACB=a,tan a=3/4,EH和HF是方程x^2-(k+2)x+4k=0的两个实数根.(1)求EH和HF的长;(2
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![已知,三角形ABC内接于圆O,AD是圆O直径,点E、F分别在AB、AC的延长线上,EF交圆O于M、N,交AD与点H,H是OD的中点,弧MD=弧DN,EH-HF=2,设角ACB=a,tan a=3/4,EH和HF是方程x^2-(k+2)x+4k=0的两个实数根.(1)求EH和HF的长;(2](/uploads/image/z/12516747-51-7.jpg?t=%E5%B7%B2%E7%9F%A5%2C%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E5%86%85%E6%8E%A5%E4%BA%8E%E5%9C%86O%2CAD%E6%98%AF%E5%9C%86O%E7%9B%B4%E5%BE%84%2C%E7%82%B9E%E3%80%81F%E5%88%86%E5%88%AB%E5%9C%A8AB%E3%80%81AC%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%B8%8A%2CEF%E4%BA%A4%E5%9C%86O%E4%BA%8EM%E3%80%81N%2C%E4%BA%A4AD%E4%B8%8E%E7%82%B9H%2CH%E6%98%AFOD%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E5%BC%A7MD%3D%E5%BC%A7DN%2CEH-HF%3D2%2C%E8%AE%BE%E8%A7%92ACB%3Da%2Ctan+a%3D3%2F4%2CEH%E5%92%8CHF%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2-%28k%2B2%29x%2B4k%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9.%281%29%E6%B1%82EH%E5%92%8CHF%E7%9A%84%E9%95%BF%3B%282)
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