X3299

INTERSECTION OF LINES X35X_372 AND X36X_371

X3299 = isogonal conjugate of X3300
< 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, 6 }: Incenter–Symmedian Line { 35, 372 }: Central Line L(35, 372) { 36, 371 }: Central Line L(36, 371) { 42, 589 }: Central Line L(42, 589) { 47, 605 }: Central Line L(47, 605) { 482, 651 }: Central Line L(482, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3300 = ISOGONAL CONJUGATE OF X(3299) (0.5513, 0.2121) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (0.6340, 0.4099) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_482 = 2nd EPPSTEIN POINT (0.5835, 0.2611) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_3299 = INTERSECTION OF LINES X(35)X(372) AND X(36)X(371) (0.5895, 0.2547) A B C X3300 X1 X6 X35 X372 X36 X371 X42 X589 X47 X605 X482 X651 X3299 (a, b, c) = (5, 6, 7) | AB = 1

X3299 (INTERSECTION OF LINES X35X_372 AND X36X_371) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + 2 \sin A : 1 + 2 \sin B : 1 + 2 \sin C\)
Barycentrics: \((1 + 2 \sin A)(\sin A) : (1 + 2 \sin B)(\sin B) : (1 + 2 \sin C)(\sin C)\)
Search Value (6, 9, 13): \(1.286267941887\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a + R : b +R : c + R\)

▸ Incident Central Lines7 lines

{1, 6}, {35, 372}, {36, 371}, {42, 589}, {46, 1702}, {47, 605}, {482, 651}

▸ Functional Relations2 relations