X993

MIDPOINT OF X1 AND X63

X993 is the midpoint of X1 and X63.
< 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) { 1, 63 }: Central Line L(1, 63) { 3, 10 }: Central Line L(3, 10) { 1, 21 }: Central Line L(1, 21) { 2, 36 }: Central Line L(2, 36) { 8, 35 }: Central Line L(8, 35) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_8 = NAGEL POINT (0.4694, 0.1333) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) A B C X1 X63 X3 X10 X21 X2 X36 X8 X35 X993 (a, b, c) = (5, 6, 7) | AB = 1

X993 (MIDPOINT OF X1 AND X63) 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 \(f(a,b,c) = a^{3} - a(b^{2} + c^{2}) - bc(b + c)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(3.782604541465\)
▸ Linear Combinations1 combination
▸ Incident Central Lines15 lines

{1, 21}, {2, 36}, {3, 10}, {8, 35}, {9, 48}, {32, 1107}, {55, 519}, {56, 226}, {75, 99}, {87, 106}, {238, 995}, {495, 529}, {516, 1012}, {527, 551}, {912, 960}

▸ Functional Relations4 relations