Search results
Results from the WOW.Com Content Network
The Nagel triangle or extouch triangle of is denoted by the vertices , , and that are the three points where the excircles touch the reference and where is opposite of , etc. This T A T B T C {\displaystyle \triangle T_{A}T_{B}T_{C}} is also known as the extouch triangle of A B C {\displaystyle \triangle ABC} .
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).
In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is + + = +, where r is the inradius and R is the circumradius of the triangle.
where r is the inradius, and s is the semiperimeter (in fact, ... In 1885, Baker [19] gave a collection of over a hundred distinct area formulas for the triangle ...
All triangles can have an incircle, but not all quadrilaterals do. ... where s is the semiperimeter and r is the inradius. Another formula is [7] = ...
This formula only works in three ... above is the area of the triangle, by Heron's formula . [5] ... hence the circumradius is at least twice the inradius (Euler's ...
A triangle is a polygon with three corners and ... Its radius is called the inradius. ... is a formula for finding the area of a triangle from the lengths of its ...
Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that