X3244

REFLECTION OF X10 IN X1

X3244 is the reflection of X10 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) { 10, 1 }: Nagel Line { 1, 2 }: Nagel Line { 58, 643 }: Central Line L(58, 643) { 382, 515 }: Central Line L(382, 515) { 517, 550 }: Central Line L(517, 550) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA (0.0142, 0.3704) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_3244 = REFLECTION OF X(10) IN X(1) (0.6224, 0.2833) A B C X10 X1 X2 X58 X643 X382 X515 X517 X550 X3244 (a, b, c) = (5, 6, 7) | AB = 1

X3244 (REFLECTION OF X10 IN X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(4a - b - c) : :\)
Barycentrics: \(4a - b - c : 4b - c - a : 4c - a - b\)
Search Value (6, 9, 13): \(0.281718084910\)
▸ Alternate Coordinates1 form

  • Trilinears: \(5 r - 2 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines15 lines

{1, 2}, {6, 2325}, {9, 2137}, {58, 643}, {65, 1317}, {79, 1320}, {382, 515}, {516, 944}, {517, 550}, {546, 946}, {950, 2098}, {996, 2334}, {1018, 1475}, {1100, 2321}, {1126, 1222}

▸ Functional Relations4 relations

Notes

Let OA be the circle centered at the A-vertex of the excenters-reflections triangle and passing through A; define OB and OC cyclically. X3244 is the radical center of OA, OB, OC. (Randy Hutson, August 28, 2020)