X3338

INTERSECTION OF LINES X1X_3 AND X7X_90

X3338 = reflection of X1 in X3304
< 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, 3304 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 7, 90 }: Central Line L(7, 90) { 9, 583 }: Central Line L(9, 583) { 58, 614 }: Central Line L(58, 614) 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_3304 = INTERSECTION OF LINES X(1)X(3) AND X(495)X(499) (0.5843, 0.2569) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_9 = MITTENPUNKT (0.5110, 0.1615) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_3338 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(90) (0.5971, 0.2805) A B C X1 X3304 X3 X7 X90 X9 X583 X58 X614 X3338 (a, b, c) = (5, 6, 7) | AB = 1

X3338 (INTERSECTION OF LINES X1X_3 AND X7X_90) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a - b + c)(a + b - c)(a + b + c) + 2abc ::\)
Search Value (6, 9, 13): \(0.852971714433\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(2 s (b c - b s - c s + s^{2}) + R S : :\)

  • Trilinears: \(r_{a} + R : :\), where \(r_{a}\), \(r_{b}\), \(r_{c}\) are the exradii

▸ Incident Central Lines26 lines

{1, 3}, {7, 90}, {9, 583}, {38, 975}, {58, 614}, {63, 1125}, {84, 1699}, {169, 1475}, {226, 499}, {255, 1471}, {388, 1737}, {474, 518}, {496, 1836}, {497, 1770}, {553, 946}, {584, 1449}, {990, 1717}, {1056, 1788}, {1106, 1448}, {1210, 1478}, {1398, 1905}, {1435, 1838}, {1452, 1870}, {1468, 1718}, {1537, 1768}, {1723, 2260}

▸ Functional Relations3 relations