X375

CENTROID OF THE PEDAL TRIANGLE OF X10

X375 is the centroid of the pedal triangle of X10.
< 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, 210 }: Central Line L(51, 210) { 44, 181 }: Central Line L(44, 181) { 354, 373 }: Central Line L(354, 373) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_354 = WEILL POINT (0.5823, 0.2533) X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_375 = CENTROID OF THE PEDAL TRIANGLE OF X(10) (0.5509, 0.2326) A B C X51 X210 X44 X181 X354 X373 X375 (a, b, c) = (5, 6, 7) | AB = 1

X375 (CENTROID OF THE PEDAL TRIANGLE OF X10) 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 \(f(a,b,c) = 2bc(b + c) + ca(c + a)\cos C + ab(a + b)\cos B\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.037957695106\)
▸ Incident Central Lines3 lines

{44, 181}, {51, 210}, {354, 373}

▸ Functional Relations1 relation