By Nazrul Islam
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Extra resources for Tensors and Their Applications
The centers and radii of the excircles of a triangle are called the triangle excenters and exradii. The incenter and excenters of a triangle, shown in Fig. 11, are equidistant from the triangles sides. Let E be an incenter or an excenter of a triangle A1 A2 A3 , Fig. 16, p. 46. 7, p. 145) is clearly convenient. Let E represent each of the incenter and excenters Ek , k = 0, 1, 2, 3, of a triangle A1 A2 A3 in a Euclidean n-space Rn , shown in Fig. 11 for n = 2. (1) The distance of E from the line LA1 A2 that passes through points A1 and A2 , Fig.
Let A1 and A2 be any two distinct points of a Euclidean space Rn , and let LA1 A2 be the line passing through these points. Furthermore, let A3 be any point of the space that does not lie on LA1 A2 , as shown in Fig. 4. Then, in the notation of Fig. 12 (Point to Line Distance). Let A1 and A2 be any two distinct points of a Euclidean space Rn , and let LA1 A2 be the line passing through these points. Furthermore, let A3 be any point of the space that does not lie on LA1 A2 , as shown in Fig. 4. Then, in the notation of Fig.
42. The tangency point T33 is the perpendicular projection of the point E3 on the line LA1 A2 that passes through the points A1 and A2 , Fig. 11. 76), p. 7, p. 154). 160) Now let T32 be the tangency point where the A3 -excircle meets the extension of the triangle side A1 A3 , as shown in Fig. 11, p. 42. The tangency point T32 is the perpendicular projection of the point E3 on the line LA1 A3 that passes through the points A1 and A3 , Fig. 11. 76), p. 163) Finally, let T31 be the tangency point where the A3 -excircle meets the extension of the triangle side A2 A3 , as shown in Fig.
Tensors and Their Applications by Nazrul Islam