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An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle. Thus, the solutions may be found by sliding a circle of constant radius between two parallel lines until it contacts the transformed third circle.
Casey's theorem; Circle packing theorem; Clifford's circle theorems; ... Tangent–secant theorem This page was last edited on 2 January 2023, at 16:54 (UTC). ...
Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. C.
In the special cases of one of the diagonals or sides being a diameter of the circle, this theorem gives rise directly to the angle sum and difference trigonometric identities. [17] The relationship follows most easily when the circle is constructed to have a diameter of length one, as shown here.
The circle packing theorem was first proved by Paul Koebe. [17] William Thurston [1] rediscovered the circle packing theorem, and noted that it followed from the work of E. M. Andreev. Thurston also proposed a scheme for using the circle packing theorem to obtain a homeomorphism of a simply connected proper subset of the plane onto the interior ...
Illustration of the sine and tangent inequalities. The figure at the right shows a sector of a circle with radius 1. The sector is θ/(2 π) of the whole circle, so its area is θ/2. We assume here that θ < π /2. = = = =