X606

INTERSECTION OF LINES X371X_601 AND X372X_602

X606 = isogonal conjugate of isotomic conjugate of X3084
< 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, 601 }: Central Line L(371, 601) { 372, 602 }: Central Line L(372, 602) { 590, 750 }: Central Line L(590, 750) { 615, 748 }: Central Line L(615, 748) 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_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_590 = ISOGONAL CONJUGATE OF X(588) (0.6000, 0.2672) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) A B C X6 X31 X371 X601 X372 X602 X590 X750 X615 X748 X606 (a, b, c) = (5, 6, 7) | AB = 1

X606 (INTERSECTION OF LINES X371X_601 AND X372X_602) 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): \(2.279982138377\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines5 lines

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

▸ Functional Relations2 relations

  • X606 = isogonal conjugate of isotomic conjugate of X3084

  • X606 = isogonal conjugate of polar conjugate of X6213