阿氏圆和蒙日圆
说起圆大家都不陌生,在高中有这么两个圆有很多好的结论,一个是阿氏圆一个是蒙日圆。阿氏圆,熟悉我几何数学公众号的都清楚其在初中的一些考法。今天把这两种圆汇总一下。
阿氏圆:
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这个公式还是挺复杂的,记不住怎么办嘛?可以临场推导一下,或计算一下。怎么计算,可以利用如下等等性质:
性质1:
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性质2:
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性质3:
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性质4:
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性质5:
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阿氏圆的题目,模型识别的关键是“到定点距离比为定值”,或是需要转化比值的类似初中的情况。
蒙日圆:
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特殊的:
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推广到:
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P轨迹只能在圆弧一部分,并不能覆盖整圆
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甚至a<b时,实际的圆是不存在的!!!
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这时候如果非得有一个圆是蒙日圆,那就是半径为虚数的虚圆
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抛物线
有没有蒙日圆?没有,但是有类似的蒙日线!
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以上命题逆命题也是成立的!!!
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所以做题的时候,蒙日圆的模型识别就是“切线垂直”
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例题就不举例了,有兴致可以自己编几道题
本次(以及以往)所有做图和源文件,将分享在QQ群文件
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