diametral points

Two points P1 and P2 on the circumferenceMathworldPlanetmath of a circle (or on a sphere) are diametral, if the line segmentMathworldPlanetmath P1P2 connecting them passes through the centre of the circle (resp. the sphere), i.e. is a diametre (http://planetmath.org/DiameterMathworldPlanetmathPlanetmath). Equivalently, the shortest distanceMathworldPlanetmath of the diametral points P1 and P2 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 c is a diametral circle of a given circle c0, if c intersects c0 diametrically, i.e. in two diametral points of c0.

If the equation of c0 is  (x-x0)2+(y-y0)2=r2  and  (a,b)  is inside c0, then the equation of the diametral circle c with centre  (a,b)  is given by

Title diametral points
Canonical name DiametralPoints
Date of creation 2013-03-22 18:32:14
Last modified on 2013-03-22 18:32:14
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Definition
Classification msc 51N20
Classification msc 51M04
Related topic Antipodal
Defines diametral
Defines diametral circle