X3301

INTERSECTION OF LINES X35X_371 AND X36X_372

X3301 = isogonal conjugate of X3302
< 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, 371 }: Central Line L(35, 371) { 36, 372 }: Central Line L(36, 372) { 42, 588 }: Central Line L(42, 588) { 47, 606 }: Central Line L(47, 606) { 481, 651 }: Central Line L(481, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3302 = ISOGONAL CONJUGATE OF X(3301) (0.4643, 0.1528) 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_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_588 = 1st KENMOTU-VAN LAMOEN POINT (0.5810, 0.2407) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) X_481 = 1st EPPSTEIN POINT (0.6148, 0.3335) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_3301 = INTERSECTION OF LINES X(35)X(371) AND X(36)X(372) (0.6402, 0.3150) A B C X3302 X1 X6 X35 X371 X36 X372 X42 X588 X47 X606 X481 X651 X3301 (a, b, c) = (5, 6, 7) | AB = 1

X3301 (INTERSECTION OF LINES X35X_371 AND X36X_372) 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): \(-0.855544800756\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines7 lines

{1, 6}, {35, 371}, {36, 372}, {42, 588}, {46, 1703}, {47, 606}, {481, 651}

▸ Functional Relations2 relations