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Some examples of theorem configuration changing the radius of the first circle. In the last configuration the circles are pairwise coincident. In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the ...
Draw three circumcircles (Miquel's circles) to triangles AB´C´, A´BC´, and A´B´C. Miquel's theorem states that these circles intersect in a single point M, called the Miquel point. In addition, the three angles MA´B, MB´C and MC´A (green in the diagram) are all equal, as are the three supplementary angles MA´C, MB´A and MC´B. [2] [3]
added angles between points and the miquel point: 20:58, 24 February 2009: 200 × 180 (16 KB) Inductiveload {{Information |Description={{en|1=A diagram showing en:Miquel's theorem - if three points A', B', C' are on the sides of a triangle ''ABC'', then the circles centred on the vertices of the triangle passing through the two points on the ...
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Lester's theorem – Several points associated with a scalene triangle lie on the same circle; Milne-Thomson circle theorem; Miquel's theorem – Concerns 3 circles through triples of points on the vertices and sides of a triangle; Monge's theorem – The intersections of the 3 pairs of external tangent lines to 3 circles are collinear
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Six Flags opened in 1961 in Arlington. These photos from the Star-Telegram show long-gone rides, historic moments and fun memories from the 1960s into into 2010s.
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...