Three points in space determine the coordinates and radius of the circle center

question:

Known three-point coordinates in space:
$P_1(x_1,{and}_1,{With}_1)$
$P_2(x_2,{and}_2,{With}_2)$
$P_3(x_3,{and}_3,{With}_3)$
Find the coordinates and radius of the center point of the circle determined by the three points.

analyze:

Restrictions:

• three points coplanar
• The distances between the three points and the center coordinates of the space circle are equal

Solution:

Attached:

Solving a system of linear algebraic equations:


Solving:

Reference:
Three points in space determine the coordinates of the center of the circle