orthogonal circles
Two circles intersecting orthogonally (http://planetmath.org/ConvexAngle) are orthogonal curves and called orthogonal circles of each other.
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(1) |
is the condition of the orthogonality (http://planetmath.org/OrthogonalCurves) of those circles.
The equation (1) tells that the centre of one circle is always outside its orthogonal circle. If is an arbitrary point outside the circle , one can always draw with that point as centre the orthogonal circle of this circle: its radius is the limited tangent from to the given circle. The square (http://planetmath.org/SquareOfANumber) of the limited tangent is equal to the power of the point with respect to the circle and thus . Accordingly, the equation of the orthogonal circle is
One of two orthogonal (http://planetmath.org/Orthogonal) circles harmonically any diameter of the other circle.
Title | orthogonal circles |
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Canonical name | OrthogonalCircles |
Date of creation | 2013-03-22 17:41:32 |
Last modified on | 2013-03-22 17:41:32 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 7 |
Author | pahio (2872) |
Entry type | Topic |
Classification | msc 51N20 |
Related topic | PerpendicularityInEuclideanPlane |
Defines | orthogonal circle |