X3867

PERSPECTOR OF ABC AND T(a², a² + c²)

X3867 is the perspector of ABC and t(a², a² + c²).
< 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) { 4, 6 }: Van Aubel Line { 141, 427 }: Central Line L(141, 427) { 428, 597 }: Central Line L(428, 597) { 511, 1595 }: Central Line L(511, 1595) { 25, 3589 }: Central Line L(25, 3589) { 1350, 3088 }: Central Line L(1350, 3088) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_597 = MIDPOINT OF X(2) AND X(6) (0.5687, 0.2336) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1595 = POINT CHELEB I (0.6047, 0.3760) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_3589 = ISOGONAL CONJUGATE OF X(3108) (0.5531, 0.2168) X_1350 = REFLECTION OF X(6) IN X(3) (0.4000, -0.0631) X_3088 = INTERSECTION OF LINES X(2)X(3) AND X(33)X(3086) (0.5981, 0.3588) X_3867 = PERSPECTOR OF ABC AND T(a2, a2 + c2) (0.6114, 0.3871) A B C X4 X6 X141 X427 X428 X597 X511 X1595 X25 X3589 X1350 X3088 X3867 (a, b, c) = (5, 6, 7) | AB = 1

X3867 (PERSPECTOR OF ABC AND T(a², a² + c²)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b^{2} + c^{2})(a^{2} + b^{2} - c^{2})(a^{2} - b^{2} + c^{2})/(3a^{2} + b^{2} + c^{2})\)
Search Value (6, 9, 13): \(-13.458126292452\)
▸ Incident Central Lines6 lines

{4, 6}, {25, 3589}, {141, 427}, {428, 597}, {511, 1595}, {1350, 3088}