X288

CEVAPOINT OF X6 AND X54

X288 is the cevapoint of X6 and X54.
< 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) { 51, 54 }: Central Line L(51, 54) { 97, 216 }: Central Line L(97, 216) { 53, 275 }: Central Line L(53, 275) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_54 = KOSNITA POINT (0.5880, 0.2176) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_97 = ISOGONAL CONJUGATE OF X(53) (0.4798, 0.0756) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_288 = CEVAPOINT OF X(6) AND X(54) (0.5936, 0.2442) A B C X6 X54 X51 X97 X216 X53 X275 X288 (a, b, c) = (5, 6, 7) | AB = 1

X288 (CEVAPOINT OF X6 AND X54) 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 \(f(A,B,C) = [\sec(B - C)]/[b \cos(C - A) + c \cos(B - A)]\)
Barycentrics: \(a/(b \sec(A - B) + c \sec(A - C)) : :\)
Search Value (6, 9, 13): \(0.255273525396\)
▸ Incident Central Lines3 lines

{51, 54}, {53, 275}, {97, 216}

▸ Functional Relations3 relations