X3339

INTERSECTION OF LINES X1X_3 AND X7X_10

X3339 = reflection of X1 in X3333
< 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, 3333 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 7, 10 }: Central Line L(7, 10) { 388, 533 }: Central Line L(388, 533) { 169, 1046 }: Central Line L(169, 1046) 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_3333 = POHOATA POINT (0.5899, 0.2671) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_533 = DIRECTION OF VECTOR AX + BX + CX, where X = X(18) (0.0625, -0.1448) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_3339 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(10) (0.6083, 0.3010) A B C X1 X3333 X3 X7 X10 X388 X533 X169 X1046 X3339 (a, b, c) = (5, 6, 7) | AB = 1

X3339 (INTERSECTION OF LINES X1X_3 AND X7X_10) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a - b + c)(a + b - c)(a + b + c) + (r/R)abc : :\)
Search Value (6, 9, 13): \(0.459600501061\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos A - 3 \cos B - 3 \cos C - 1 : :\)

▸ Incident Central Lines22 lines

{1, 3}, {7, 10}, {109, 1451}, {169, 1046}, {196, 1838}, {208, 1844}, {221, 1203}, {223, 2939}, {269, 1126}, {386, 1042}, {388, 533}, {516, 938}, {518, 1706}, {527, 2551}, {595, 1471}, {758, 936}, {959, 978}, {1210, 1699}, {1406, 2003}, {1698, 1788}, {1721, 2955}, {1767, 2956}

▸ Functional Relations1 relation

Notes

See the note at X3333.