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Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out ...
An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides, and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle. Further, it allows one to prove ...
The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. All circles are similar. [12] A circle circumference and radius are ...
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 .
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]
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