已知A(3,5)B(-1,3)C(-3,1)为三角形ABC的三个顶点,O M N分别为边AB BC CA的中点,求三角形OMN的外接圆方程
已知A(3,5)B(-1,3)C(-3,1)为三角形ABC的三个顶点,O M N分别为边AB BC CA的中点,求三角形OMN的外接圆方程
数学人气:204 ℃时间:2019-10-17 04:46:23
优质解答
由O、M、N分别为中点,得O(1,4)、M(-2,2)、N(0,3),根据圆标准公式(X-X1)^2+(Y-Y1)^2=R^2,将O、M、N分别代入方程,组成三元二次方程组,解得X1=-3.5,Y1=7.5,R=5.7,所以圆心为(-3.5,7.5)半径为5.7,方程为(X+3.5)^2+(Y-7.5)^2=5.7^2
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