X2190

X2-ISOCONJUGATE OF X216

X2190 = crosspoint of X1 and X47 wrt excentral triangle
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 54, 65 }: Central Line L(54, 65) { 47, 91 }: Central Line L(47, 91) { 31, 158 }: Central Line L(31, 158) { 10, 275 }: Central Line L(10, 275) { 82, 240 }: Central Line L(82, 240) { 75, 255 }: Central Line L(75, 255) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_2190 = -ISOCONJUGATE OF X(216) (0.6223, 0.3794) A B C X54 X65 X47 X91 X31 X158 X10 X275 X82 X240 X75 X255 X2190 (a, b, c) = (5, 6, 7) | AB = 1

X2190 (X2-ISOCONJUGATE OF X216) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A \sec(B - C) : :\)
Barycentrics: \(\tan A \sec(B - C) : :\)
Search Value (6, 9, 13): \(-2.998728354174\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(1/(\cos(2B) + \cos(2C)) : :\)

  • Trilinears: \(1/(\tan B \tan C + 1) : :\)

▸ Incident Central Lines11 lines

{1, 1748}, {10, 275}, {19, 2148}, {31, 158}, {47, 91}, {54, 65}, {75, 255}, {82, 240}, {162, 2166}, {270, 759}, {1973, 2186}

▸ Functional Relations4 relations

Notes

Let A'B'C' be the circumorthic triangle. Let A″ be the trilinear product B'*C', and define B″ and C″ cyclically. A″, B″, C″ are collinear on line X810X2616. The lines AA″, BB″, CC″ concur in X2190. (Randy Hutson, July 20, 2016)

Let P1 and P2 be the two points on the circumcircle whose Steiner lines are tangent to the circumcircle. Let Q1 and Q2 be the respective points of tangency. Q1 and Q2 are also the circumcircle intercepts of line X186X523. X2190 is the trilinear product of Q1 and Q2. See also X8882. (Randy Hutson, July 20, 2016)

Let Refa be the reflection of A in BC. Let AB, AC be the reflections of Refa in CA and AB, resp. Let A″ be the trilinear product AB*AC. Define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X2190. (Randy Hutson, July 11, 2019)