X1483

REFLECTION OF X5 IN X1

X1483 is the reflection of X5 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) { 5, 1 }: Feuerbach Line { 3, 145 }: Central Line L(3, 145) { 8, 140 }: Central Line L(8, 140) { 40, 548 }: Central Line L(40, 548) { 10, 632 }: Central Line L(10, 632) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_8 = NAGEL POINT (0.4694, 0.1333) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_40 = BEVAN POINT (0.4286, -0.0292) X_548 = MIDPOINT OF X(5) AND X(20) (0.4719, 0.0286) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_632 = 9/10*OG (0.5337, 0.1902) X_1483 = REFLECTION OF X(5) IN X(1) (0.5867, 0.2177) A B C X5 X1 X3 X145 X8 X140 X40 X548 X10 X632 X1483 (a, b, c) = (5, 6, 7) | AB = 1

X1483 (REFLECTION OF X5 IN X1) 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 \(f(a,b,c) = 4r - R \cos(B - C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.827745277279\)
▸ Incident Central Lines9 lines

{1, 5}, {3, 145}, {8, 140}, {10, 632}, {30, 944}, {40, 548}, {517, 550}, {518, 1353}, {519, 549}

▸ Functional Relations3 relations

  • X1483 = midpoint of Xi and Xj for these (i,j): (3, 145), (944, 1482)

  • X1483 = reflection of Xi in Xj for these (i,j): (5, 1), (8, 140)

  • X1483 = X5-of-5th-mixtilinear-triangle