X2670

MIDPOINT OF PU(85)

X2670 is the midpoint of pu(85).
< 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) { 1084, 1100 }: Central Line L(1084, 1100) { 511, 2653 }: Central Line L(511, 2653) { 798, 2667 }: Central Line L(798, 2667) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1084 = CROSSPOINT OF X(2) AND X(512) (0.8090, 0.1525) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2653 = MIDPOINT OF PU(81) (0.5918, 0.2602) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_2667 = SUM OF PU(85) (0.5803, 0.2413) X_2670 = MIDPOINT OF PU(85) (0.5803, 0.2412) A B C X1084 X1100 X511 X2653 X798 X2667 X2670 (a, b, c) = (5, 6, 7) | AB = 1

X2670 (MIDPOINT OF PU(85)) 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 \(f(a,b,c) = k(a,b,c)ca/(c + a) + h(a,b,c)ba/(b + a)\), where \(h(a,b,c) = ca^{2}/(c + a) + ab^{2}/(a + b) + bc^{2}/(b + c)\), and \(k(a,b,c) = ba^{2}/(b + a) + cb^{2}/(c + b) + ac^{2}/(a + c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.463552809840\)
▸ Incident Central Lines3 lines

{511, 2653}, {798, 2667}, {1084, 1100}