X609

INTERSECTION OF LINES X1X_32 AND X6X_36

< 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, 32 }: Central Line L(1, 32) { 6, 36 }: Central Line L(6, 36) { 41, 58 }: Central Line L(41, 58) { 31, 101 }: Central Line L(31, 101) { 33, 112 }: Central Line L(33, 112) { 251, 614 }: Central Line L(251, 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_609 = INTERSECTION OF LINES X(1)X(32) AND X(6)X(36) (0.6191, 0.3028) A B C X1 X32 X6 X36 X41 X58 X31 X101 X33 X112 X251 X614 X609 (a, b, c) = (5, 6, 7) | AB = 1

X609 (INTERSECTION OF LINES X1X_32 AND X6X_36) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\operatorname{area} + a^{2} \sin A : \operatorname{area} + b^{2} \sin B : \operatorname{area} + c^{2} \sin C\)
Barycentrics: \(a(\operatorname{area} + a^{2} \sin A) : b(\operatorname{area} + b^{2} \sin B) : c(\operatorname{area} + c^{2} \sin C)\)
Search Value (6, 9, 13): \(0.580273707913\)
▸ Incident Central Lines7 lines

{1, 32}, {6, 36}, {31, 101}, {33, 112}, {41, 58}, {251, 614}, {995, 1055}