Question

如图所示,已知圆O和圆O上一点A,求以点A为一端点的弦的中点的轨迹

Answer 1

以A为原点,AO为x轴建立坐标系,设圆O半径为r,弦中点C(x,y),则：OC^2+CA^2=OA^2

===> x^2+y^2+(x-r)^2+y^2=r^2

===> 2x^2-2rx+2y^2=0

===> x^2-rx+y^2=0

===> [x-(r/2)]^2+y^2=r^2/4

所以,圆心C的轨迹就是以OA中点为圆心,半径=OA/2的圆.