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In general, the same inversion transforms the given circle C 1 and C 2 into two new circles, c 1 and c 2. Thus, the problem becomes that of finding a solution line tangent to the two inverted circles, which was solved above. There are four such lines, and re-inversion transforms them into the four solution circles of the original Apollonius ...
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A general Apollonius problem can be transformed into the simpler problem of circle tangent to one circle and two parallel lines (itself a special case of the LLC special case). To accomplish this, it suffices to scale two of the three given circles until they just touch, i.e., are tangent.
The same inversion transforms the third circle into another circle. The solution of the inverted problem must either be (1) a straight line parallel to the two given parallel lines and tangent to the transformed third given circle; or (2) a circle of constant radius that is tangent to the two given parallel lines and the transformed given circle.
Ordinary trigonometry studies triangles in the Euclidean plane .There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions [broken anchor], definitions via differential equations [broken anchor], and definitions using functional equations.
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Angular unit. Degree (angle) Gon (angle) (aka Grad, Gradian) Radian; Turn (angle) Brocard points; Chord (geometry) Circle (also see List of circle topics) Unit circle; Hypotenuse; Opposites post; π (pi) Ptolemy's theorem; Pythagorean theorem; Regiomontanus' angle maximization problem; Thales' theorem; Trigonometric function; Trigonometry of a ...