diametral points
Two points and on the circumference of a circle (or on a sphere) are diametral, if the line segment
connecting them passes through the centre of the circle (resp. the sphere), i.e. is a diametre (http://planetmath.org/Diameter
). Equivalently, the shortest distance
of the diametral points and on the circle is maximal on the circle (resp. on the sphere), namely a half of the perimetre (http://planetmath.org/Perimeter).
It’s easily justified that a point of a circle (resp. a sphere) has exactly one diametral point.
A circle is a diametral circle of a given circle , if intersects diametrically, i.e. in two diametral points of .
If the equation of is and is inside , then the equation of the diametral circle with centre is given by