X374

CENTROID OF THE PEDAL TRIANGLE OF X9

X374 is the centroid of the pedal triangle of X9.
< 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) { 44, 65 }: Central Line L(44, 65) { 51, 210 }: Central Line L(51, 210) { 6, 354 }: Central Line L(6, 354) { 9, 517 }: Central Line L(9, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_354 = WEILL POINT (0.5823, 0.2533) X_9 = MITTENPUNKT (0.5110, 0.1615) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_374 = CENTROID OF THE PEDAL TRIANGLE OF X(9) (0.5449, 0.2238) A B C X44 X65 X51 X210 X6 X354 X9 X517 X374 (a, b, c) = (5, 6, 7) | AB = 1

X374 (CENTROID OF THE PEDAL TRIANGLE OF X9) 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 \(f(a,b,c) = 2b + 2c - 3a + (c + a)\cos C + (b + a)\cos B\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.141317916799\)
▸ Incident Central Lines5 lines

{6, 354}, {9, 517}, {44, 65}, {51, 210}, {966, 3740}