X2642

SUM OF PU(79)

X2642 = isogonal conjugate of X36085
< 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, 513 }: Central Line L(44, 513) { 163, 662 }: Central Line L(163, 662) { 900, 1213 }: Central Line L(900, 1213) { 665, 2092 }: Central Line L(665, 2092) { 1910, 2159 }: Central Line L(1910, 2159) { 1931, 2641 }: Central Line L(1931, 2641) 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_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_2092 = DANNEELS-APOLLONIUS PERSPECTOR (0.5833, 0.2396) X_1910 = TRILINEAR POLE OF PU(23) (0.9516, -0.2978) X_2159 = -ISOCONJUGATE OF X(30) (0.8357, -0.4858) X_1931 = CROSSDIFFERENCE OF PU(32) (1.7418, 1.7715) X_2641 = MIDPOINT OF PU(78) (1.9999, 2.1774) X_2642 = SUM OF PU(79) (2.3576, 1.9826) A B C X44 X513 X163 X662 X900 X1213 X665 X2092 X1910 X2159 X1931 X2641 X2642 (a, b, c) = (5, 6, 7) | AB = 1

X2642 (SUM OF PU(79)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\cot C - \cot A) + 1/(\cot B - \cot A) : :\)
Search Value (6, 9, 13): \(-8.543721359192\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((b^{2} - c^{2})(2a^{2} - b^{2} - c^{2}) : :\) (M. Iliev, 5/13/07)

  • Trilinears: \((\cot B - \cot C)(2 \cot A - \cot B - \cot C) : :\) (R. Hutson, 8/19/19)

▸ Incident Central Lines6 lines

{44, 513}, {163, 662}, {665, 2092}, {900, 1213}, {1910, 2159}, {1931, 2641}

▸ Functional Relations2 relations

  • X2642 = isogonal conjugate of X36085

  • X2642 = PU(79)-harmonic conjugate of X2643