如图,点abcd都在圆上,弧BD=弧DC,AD与BC相交于点E(1)图中一共有____对相似三角形(2)若AB=6,AC=4,AE=3,试求AD,CD的长 上午一节课45分钟老师都没做出来, (YongDingSanZhong)F为E,画错了
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![如图,点abcd都在圆上,弧BD=弧DC,AD与BC相交于点E(1)图中一共有____对相似三角形(2)若AB=6,AC=4,AE=3,试求AD,CD的长 上午一节课45分钟老师都没做出来, (YongDingSanZhong)F为E,画错了](/uploads/image/z/14605329-57-9.jpg?t=%E5%A6%82%E5%9B%BE%2C%E7%82%B9abcd%E9%83%BD%E5%9C%A8%E5%9C%86%E4%B8%8A%2C%E5%BC%A7BD%3D%E5%BC%A7DC%2CAD%E4%B8%8EBC%E7%9B%B8%E4%BA%A4%E4%BA%8E%E7%82%B9E%EF%BC%881%EF%BC%89%E5%9B%BE%E4%B8%AD%E4%B8%80%E5%85%B1%E6%9C%89____%E5%AF%B9%E7%9B%B8%E4%BC%BC%E4%B8%89%E8%A7%92%E5%BD%A2%EF%BC%882%EF%BC%89%E8%8B%A5AB%3D6%2CAC%3D4%2CAE%3D3%2C%E8%AF%95%E6%B1%82AD%2CCD%E7%9A%84%E9%95%BF++++++++%E4%B8%8A%E5%8D%88%E4%B8%80%E8%8A%82%E8%AF%BE45%E5%88%86%E9%92%9F%E8%80%81%E5%B8%88%E9%83%BD%E6%B2%A1%E5%81%9A%E5%87%BA%E6%9D%A5%2C++++++++++%28YongDingSanZhong%29F%E4%B8%BAE%2C%E7%94%BB%E9%94%99%E4%BA%86)
如图,点abcd都在圆上,弧BD=弧DC,AD与BC相交于点E(1)图中一共有____对相似三角形(2)若AB=6,AC=4,AE=3,试求AD,CD的长 上午一节课45分钟老师都没做出来, (YongDingSanZhong)F为E,画错了
如图,点abcd都在圆上,弧BD=弧DC,AD与BC相交于点E
(1)图中一共有____对相似三角形(2)若AB=6,AC=4,AE=3,试求AD,CD的长 上午一节课45分钟老师都没做出来, (YongDingSanZhong)
F为E,画错了
如图,点abcd都在圆上,弧BD=弧DC,AD与BC相交于点E(1)图中一共有____对相似三角形(2)若AB=6,AC=4,AE=3,试求AD,CD的长 上午一节课45分钟老师都没做出来, (YongDingSanZhong)F为E,画错了
(1)按你给出的图,BD 线段没有联结,那么相似的有三对:
ABF 与 CDF ;CDF 与 ADC;ADC 与 ABF .
(2)由于 ∠B = ∠D ,∠BAF = ∠DAC (等弧所对的圆周角相等),
所以三角形 ABF 与 ADC 相似,
因此 AB/AD = AF/AC ,
所以 AD = AB*AC/AF = 6*4/3 = 8 ,则 FD = AD-AF = 8-3 = 5 ,
由于 ∠D = ∠D ,∠DAC = ∠BAD = ∠BCD ,
因此三角形 CDF 与 ADC 相似,
因此 AD/DC = DC/DF ,
所以 DC^2 = AD*DF = 8*5 = 40 ,
所以 DC = 2√10 .
答:AD = 8 ,DC = 2√10 .