X2632

DIFFERENCE OF PU(75)

X2632 = X1-Ceva conjugate of X652
< 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, 162 }: Central Line L(1, 162) { 63, 293 }: Central Line L(63, 293) { 336, 799 }: Central Line L(336, 799) { 122, 1367 }: Central Line L(122, 1367) { 520, 1364 }: Central Line L(520, 1364) { 92, 1956 }: Central Line L(92, 1956) 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_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_293 = ISOGONAL CONJUGATE OF X(240) (0.7839, -0.0636) X_336 = ISOTOMIC CONJUGATE OF X(240) (0.7020, -0.0409) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_122 = -OF-MEDIAL-TRIANGLE (0.5195, -0.0036) X_1367 = BRISSE TRANSFORM OF X(112) (0.6451, 0.0119) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_1364 = BRISSE TRANSFORM OF X(108) (0.5367, 0.6071) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1956 = TRILINEAR POLE OF PU(21) (0.6554, -0.4540) X_2632 = DIFFERENCE OF PU(75) (0.6212, 0.0090) A B C X1 X162 X63 X293 X336 X799 X122 X1367 X520 X1364 X92 X1956 X2632 (a, b, c) = (5, 6, 7) | AB = 1

X2632 (DIFFERENCE OF PU(75)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\tan C - \tan A) - 1/(\tan B - \tan A) : :\)
Search Value (6, 9, 13): \(3.612030843155\)
▸ Alternate Coordinates6 forms

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

  • Trilinears: \((\tan B - \tan C)^{2} : :\)

  • Trilinears: \((\sin 2B - \sin 2C)^{2} : :\)

  • Trilinears: \(\cos^{2} A \sin^{2}(B - C) : :\)

  • Trilinears: \([b \cos(C - A) - c \cos(B - A)]^{2} : :\)

  • Trilinears: \((distance from A to Euler line)^{2} : :\)

X2632 lies on the incentral inellipse (i.e., Hofstadter ellipse E(1/2)).

▸ Incident Central Lines11 lines

{1, 162}, {48, 2157}, {63, 293}, {92, 1956}, {122, 1367}, {336, 799}, {520, 1364}, {1096, 2184}, {2292, 2658}, {2310, 2611}, {2631, 2634}

▸ Functional Relations9 relations