You are misleading here. We can always draw a circle given three random points. If there are four random points, there is no guarantee that the fourth point is on the circle. The reason is simple. The equation of a circle is (x-a)^2 + (y-b)^2 = r^2. We just need three points to define a circle with parameters (a, b, r).
Nope it is not misleading. He was presenting a proposition that gives a necessary and sufficient condition on whether four points are on the same circle.
You didn't listen. What he did was adding a fourth point D on the circumcircle of the triangle ABC. D being concyclic with A, B and C was the beginning point. In addition, he did mention that the four points were equidistant from the circumcenter.
非常好用，四點有四個三角形，四條邊。
任何三條边，有四個選擇。
不可能吧？四点共圆删了中学平面几何还学个屁啊？据说正余弦定理搞到高中了？以前正余弦定理是初中内容。照这样趋势下去，以后初中只能教100以内的加减法了
正余弦定理很早就去高中了
以前是教多邊形共圓...
現在只剩下三角形了?
台灣還有教四邊形
有教，沒深入
任何多邊形都能分解為若干三角形……
@@tommymairo8964 說得對
任何數字都能分解為若干 1
以後只要學1就好了
因為只有三角形才會必然形成三點共圓的狀況，然而圓內接多邊形並不見得是常態。過度強調圓內接多邊形而不探討如何驗證某多邊形是否頂點共圓，反而會造成很嚴重的誤導。讓學生以為梯形箏形平行四邊形也都是共圓的。
记得三十年前 四点共圆和各种面积定理的应用是检验初中平面几何能力的灵魂 😮💨
現在還有，不過是針對程度較優秀的學生
不是叫圓內接矩形嗎，對角加起來180度
好用。
很多年前解析几何里还有关于坐标系旋转的部分，现在也不要求了。
立体几何里内容，本来就没多少，偏偏还把二面角和三垂线定理给否了。。
抱歉 以前只想着去公园， 共圆是什么东西~🤣
謝謝
四点共圆什么的先抛开一边，第一种解法是怎么想到的？这种考试之前没接触过的，考试的时候很难想象得到吧，考试的时候基本不可能做出来，只有刷题或者老师讲过这题的才会知道。
三角形APB绕点B顺时针旋转90度的三角形CMB。
橫平豎直的，直接建系……
任意不在一条直线上的4个点组成的四边形，都共圆
你在说笑吧？只听过不在直线上的三点肯定共圆。
删了四点共圆，那蝴蝶定理也没了.......
You are misleading here. We can always draw a circle given three random points. If there are four random points, there is no guarantee that the fourth point is on the circle. The reason is simple. The equation of a circle is (x-a)^2 + (y-b)^2 = r^2. We just need three points to define a circle with parameters (a, b, r).
Nope it is not misleading. He was presenting a proposition that gives a necessary and sufficient condition on whether four points are on the same circle.
You didn't listen. What he did was adding a fourth point D on the circumcircle of the triangle ABC. D being concyclic with A, B and C was the beginning point. In addition, he did mention that the four points were equidistant from the circumcenter.
台灣有
还是不知道“课本为什么删掉四点共圆”。不说四点共圆，却讲什么“8”字模型，不明所以。
三点共圆已经够了
四点共用共圆竟然被删了？
我國中生 這個沒被刪掉
@@碳烤起司吉拿 人家是中國人
课本上有圆的内接四边形知识，当老师教到这块内容时会补充四点共圆的知识，会相应地做一些四点共圆的练习，因为有些几何问题用四点共圆做真心简单。所以实际上初中老师还是会补充四点共圆的！
耸人听闻