X1203

3rd SARAGOSSA POINT OF X58

X1203 = crosspoint of X58 and X1126
< 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, 6 }: Incenter–Symmedian Line { 31, 35 }: Central Line L(31, 35) { 36, 58 }: Central Line L(36, 58) { 42, 595 }: Central Line L(42, 595) { 581, 602 }: Central Line L(581, 602) { 81, 1125 }: Central Line L(81, 1125) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1126 = ISOGONAL CONJUGATE OF X(1125) (0.5938, 0.2586) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_1203 = 3rd SARAGOSSA POINT OF X(58) (0.6034, 0.2712) A B C X58 X1126 X1 X6 X31 X35 X36 X42 X595 X581 X602 X81 X1125 X1203 (a, b, c) = (5, 6, 7) | AB = 1

X1203 (3rd SARAGOSSA POINT OF X58) 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 \(f(a,b,c) = a[(a + b + c)^{2} - bc]\) (M. Iliev, 5/13/2007)
Search Value (6, 9, 13): \(0.925898529270\)
▸ Alternate Coordinates1 form

  • Trilinears: \(as - rR : bs - rR : cs - rR\) (C. Lozada, 9/07/2013)

▸ Incident Central Lines7 lines

{1, 6}, {31, 35}, {36, 58}, {42, 595}, {81, 1125}, {580, 1064}, {581, 602}

▸ Functional Relations3 relations