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A circle not passing through O inverts to a circle not passing through O. If the circle meets the reference circle, these invariant points of intersection are also on the inverse circle. A circle (or line) is unchanged by inversion if and only if it is orthogonal to the reference circle at the points of intersection. [5] Additional properties ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles, for instance in inversive geometry, then an orthogonal pair of lines or line and circle are orthogonal generalized circles.
In this case the circle with radius zero is a double point, and thus any line passing through it intersects the point with multiplicity two, hence is "tangent". If one circle has radius zero, a bitangent line is simply a line tangent to the circle and passing through the point, and is counted with multiplicity two.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
In either case, the third circle must pass through this plane or sphere four times, without lying in it, which is impossible. [26] Another argument for the impossibility of circular realizations, by Helge Tverberg , uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to argue that the ...
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