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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.
Tangent lines to circles; Circle packing theorem, the result that every planar graph may be realized by a system of tangent circles; Hexafoil, the shape formed by a ring of six tangent circles; Feuerbach's theorem on the tangency of the nine-point circle of a triangle with its incircle and excircles; Descartes' theorem; Ford circle; Bankoff circle
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1]
Draw circle C that has PQ as diameter. Draw one of the tangents from G to circle C. point A is where the tangent and the circle touch. Draw circle D with center G through A. Circle D cuts line l at the points T1 and T2. One of the required circles is the circle through P, Q and T1. The other circle is the circle through P, Q and T2.
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). ...
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...
For every set of four mutually tangent circles, there is a second set of four mutually tangent circles that are tangent at the same six points. [ 2 ] [ 49 ] Descartes' theorem was rediscovered independently in 1826 by Jakob Steiner , [ 50 ] in 1842 by Philip Beecroft, [ 2 ] [ 49 ] and again in 1936 by Frederick Soddy . [ 51 ]