X3242

REFLECTION OF X6 IN X1

X3242 is the reflection of X6 in X1.
< 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, 1 }: Incenter–Symmedian Line { 38, 55 }: Central Line L(38, 55) { 69, 145 }: Central Line L(69, 145) { 210, 614 }: Central Line L(210, 614) { 354, 612 }: Central Line L(354, 612) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1 = INCENTER (0.5714, 0.2333) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_354 = WEILL POINT (0.5823, 0.2533) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_3242 = REFLECTION OF X(6) IN X(1) (0.5429, 0.1994) A B C X6 X1 X38 X55 X69 X145 X210 X614 X354 X612 X3242 (a, b, c) = (5, 6, 7) | AB = 1

X3242 (REFLECTION OF X6 IN X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2(a^{2} + b^{2} + c^{2}) - a(a + b + c) : :\)
Search Value (6, 9, 13): \(2.387708523848\)
▸ Linear Combinations1 combination
▸ Incident Central Lines11 lines

{1, 6}, {38, 55}, {56, 976}, {69, 145}, {210, 614}, {354, 612}, {674, 1469}, {982, 1054}, {990, 1350}, {1086, 2550}, {1219, 1257}

▸ Functional Relations3 relations