X2066

POINT CAROLI I

X2066 = cevapoint of X48 and X605
< 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) { 1, 371 }: Central Line L(1, 371) { 35, 372 }: Central Line L(35, 372) { 11, 590 }: Central Line L(11, 590) { 486, 498 }: Central Line L(486, 498) { 3, 1124 }: Central Line L(3, 1124) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1 = INCENTER (0.5714, 0.2333) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) 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_11 = FEUERBACH POINT (0.7347, 0.0667) X_590 = ISOGONAL CONJUGATE OF X(588) (0.6000, 0.2672) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_2066 = POINT CAROLI I (0.5679, 0.2199) A B C X48 X605 X6 X31 X1 X371 X35 X372 X11 X590 X486 X498 X3 X1124 X2066 (a, b, c) = (5, 6, 7) | AB = 1

X2066 (POINT CAROLI I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1 + \sin A + \cos A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.045277903180\)

X2066 lies on the hyperbola {{A, B, C,X1,X3}}.

▸ Incident Central Lines10 lines

{1, 371}, {3, 1124}, {6, 31}, {11, 590}, {35, 372}, {56, 1151}, {283, 1806}, {405, 1378}, {485, 1479}, {486, 498}

▸ Functional Relations4 relations