X1939

MIDPOINT OF PU(15)

X1939 is the midpoint of pu(15).
< 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) { 65, 650 }: Central Line L(65, 650) { 169, 1575 }: Central Line L(169, 1575) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1575 = EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES (2.5675, 1.8684) X_1939 = MIDPOINT OF PU(15) (0.6029, 0.2937) A B C X65 X650 X169 X1575 X1939 (a, b, c) = (5, 6, 7) | AB = 1

X1939 (MIDPOINT OF PU(15)) 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 \(f(a,b,c) = (a \cos B + b \cos C + c \cos A) \cos C + (a \cos C + b \cos A + c \cos B) \cos B\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.799325217718\)
▸ Incident Central Lines3 lines

{65, 650}, {169, 1575}, {1385, 2649}