X2658

SUM OF PU(83)

X2658 = X1-Ceva conjugate of X2654
< 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) { 1, 29 }: Central Line L(1, 29) { 42, 65 }: Central Line L(42, 65) { 1108, 1201 }: Central Line L(1108, 1201) { 653, 2656 }: Central Line L(653, 2656) { 2292, 2632 }: Central Line L(2292, 2632) { 2638, 2646 }: Central Line L(2638, 2646) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2654 = SUM OF PU(82) (0.5822, 0.2761) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1108 = CROSSPOINT OF X(2) AND X(84) (0.6346, 0.3084) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_2656 = TRILINEAR POLE OF PU(82) (0.6337, -0.4192) X_2292 = -ISOCONJUGATE OF X(1169) (0.5509, 0.2064) X_2632 = DIFFERENCE OF PU(75) (0.6212, 0.0090) X_2638 = DIFFERENCE OF PU(77) (0.6093, 0.0064) X_2646 = SUM OF PU(80) (0.5544, 0.2019) X_2658 = SUM OF PU(83) (0.5613, 0.1772) A B C X1 X2654 X29 X42 X65 X1108 X1201 X653 X2656 X2292 X2632 X2638 X2646 X2658 (a, b, c) = (5, 6, 7) | AB = 1

X2658 (SUM OF PU(83)) 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 \(f(A,B,C) = 1/(\sec C + \sec A) + 1/(\sec B + \sec A)\),
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.703327935575\)
▸ Incident Central Lines7 lines

{1, 29}, {42, 65}, {653, 2656}, {822, 2661}, {1108, 1201}, {2292, 2632}, {2638, 2646}

▸ Functional Relations4 relations