X3241

REFLECTION OF X2 IN X1

X3241 is the reflection of X2 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) { 2, 1 }: Nagel Line { 7, 528 }: Central Line L(7, 528) { 6, 644 }: Central Line L(6, 644) { 192, 537 }: Central Line L(192, 537) { 376, 517 }: Central Line L(376, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_537 = DIRECTION OF VECTOR AX + BX + CX, where X = X(38) (-0.0190, 0.3866) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_3241 = REFLECTION OF X(2) IN X(1) (0.6054, 0.2666) A B C X2 X1 X7 X528 X6 X644 X192 X537 X376 X517 X3241 (a, b, c) = (5, 6, 7) | AB = 1

X3241 (REFLECTION OF X2 IN X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(5a - b - c) : :\)
Barycentrics: \(5a - b - c : 5b - c - a : 5c - a - b\)
Search Value (6, 9, 13): \(0.751248226425\)
▸ Alternate Coordinates1 form

  • Trilinears: \(3 r - R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines16 lines

{1, 2}, {4, 1392}, {6, 644}, {7, 528}, {30, 944}, {149, 1478}, {192, 537}, {346, 1449}, {376, 517}, {381, 952}, {390, 527}, {518, 1992}, {529, 2098}, {956, 1621}, {1000, 2320}, {1222, 2334}

▸ Functional Relations8 relations