X605

INTERSECTION OF LINES X371X_602 AND X372X_601

X605 = isogonal conjugate of isotomic conjugate of X3083
< 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) { 6, 31 }: Central Line L(6, 31) { 371, 602 }: Central Line L(371, 602) { 372, 601 }: Central Line L(372, 601) { 590, 748 }: Central Line L(590, 748) { 615, 750 }: Central Line L(615, 750) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_590 = ISOGONAL CONJUGATE OF X(588) (0.6000, 0.2672) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) A B C X6 X31 X371 X602 X372 X601 X590 X748 X615 X750 X605 (a, b, c) = (5, 6, 7) | AB = 1

X605 (INTERSECTION OF LINES X371X_602 AND X372X_601) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(1 + \sin A) : b(1 + \sin B) : c(1 + \sin c)\)
Barycentrics: \(a^{2}(1 + \sin A) : b^{2}(1 + \sin B) : c^{2}(1 + \sin C)\)
Search Value (6, 9, 13): \(0.801159897202\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2}(S + bc) : b^{2}(S + ca) : c^{2}(S + ab)\)

▸ Incident Central Lines5 lines

{6, 31}, {371, 602}, {372, 601}, {590, 748}, {615, 750}

▸ Functional Relations4 relations