X1488

2nd STEVANOVIC POINT

X1488 = X1-cross conjugate of X174
< 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) { 1, 166 }: Central Line L(1, 166) { 57, 173 }: Central Line L(57, 173) { 145, 188 }: Central Line L(145, 188) { 558, 1143 }: Central Line L(558, 1143) { 557, 1274 }: Central Line L(557, 1274) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_174 = YFF CENTER OF CONGRUENCE (0.5813, 0.2549) X_166 = GERGONNE POINT OF EXCENTRAL TRIANGLE (0.5156, 0.1554) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_188 = 2nd MID-ARC POINT OF ANTICOMPLEMENTARY TRIANGLE (0.5245, 0.1802) X_558 = (X(1),X(57))-ANSWER TO QUESTION A (0.6164, 0.3210) X_1143 = 2nd MALFATTI-RABINOWITZ POINT (0.5857, 0.2649) X_557 = (X(1),X(9))-ANSWER TO QUESTION A (0.5314, 0.1908) X_1274 = ISOTOMIC CONJUGATE OF X(1143) (0.4773, 0.1423) X_1488 = 2nd STEVANOVIC POINT (0.5582, 0.2148) A B C X1 X174 X166 X57 X173 X145 X188 X558 X1143 X557 X1274 X1488 (a, b, c) = (5, 6, 7) | AB = 1

X1488 (2nd STEVANOVIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[1 + \sin(A/2)] : :\)
Search Value (6, 9, 13): \(2.088904139589\)
▸ Alternate Coordinates1 form
▸ Incident Central Lines6 lines

{1, 166}, {7, 2089}, {57, 173}, {145, 188}, {557, 1274}, {558, 1143}

▸ Functional Relations4 relations

  • X1488 = X1-cross conjugate of X174

  • X1488 = SS(A→Ja) of X7, where JaJbJc is the excentral triangle

  • X1488 = trilinear pole of Monge line of incircles of BCI, CAI, ABI

  • X1488 = trilinear pole of Monge line of I-excircles of BCI, CAI, ABI

Notes

Let U be the A-excenter of triangle ABC; let A' be the incenter of triangle UBC, and define B', C' cyclically. Let A″ = IA'∩BC, and define B″, C″ cyclically. The lines AA″, BB″, CC″ concur in X1488. (Milorad R. Stevanovic, Hyacinthos #7185, 5/21/03. See also X1130 and X1489.)