Information om | Engelska ordet EXCIRCLE

Exempel på hur man kan använda EXCIRCLE i en mening

• An excircle or escribed circle 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.
• There are many ways to prove Heron's formula, for example using trigonometry as below, or the incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular case of acute triangles), or as a special case of Brahmagupta's formula (for the case of a degenerate cyclic quadrilateral).
• In any triangle, any vertex and the point where the opposite excircle touches the triangle partition the triangle's perimeter into two equal lengths, thus creating two paths each of which has a length equal to the semiperimeter.
• An "external" version of this theorem, where the incircle is replaced by an excircle and the two additional circles are external to the circumcircle, is found in Shay Gueron (2002).
• Any vertex, the tangency of the opposite side with an excircle, and the Nagel point are collinear in a line called a splitter of the triangle.
• There are infinitely many decomposable, and infinitely many indecomposable, primitive Heronian (non-Pythagorean) triangles with integer radii for the incircle and each excircle.
• In that context all convex quadrilaterals have four escribed circles, but they can at most have one excircle.
• It is defined as the point of concurrence of the three line segments joining each vertex of the triangle to the points of tangency formed by the opposing excircle and a larger circle that is tangent to all three excircles.

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