X3021

5th STEVANOVIC POINT

X3021 = X7-Ceva conjugate of X3008
< 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) { 11, 55 }: Central Line L(11, 55) { 56, 1292 }: Central Line L(56, 1292) { 1, 1358 }: Central Line L(1, 1358) { 354, 1357 }: Central Line L(354, 1357) { 1317, 2826 }: Central Line L(1317, 2826) { 1361, 2814 }: Central Line L(1361, 2814) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_3008 = (GERGONNE LINE)∩(NAGEL LINE) (1.4558, 1.0998) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1292 = COLLINGS TRANSFORM OF X(55) (0.0286, 0.2974) X_1 = INCENTER (0.5714, 0.2333) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_354 = WEILL POINT (0.5823, 0.2533) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_2826 = ISOGONAL CONJUGATE OF X(2742) (0.8660, 0.6862) X_1361 = BRISSE TRANSFORM OF X(104) (0.5091, 0.4581) X_2814 = ISOGONAL CONJUGATE OF X(2730) (0.0978, -0.1889) X_3021 = 5th STEVANOVIC POINT (0.3559, 0.3226) A B C X7 X3008 X11 X55 X56 X1292 X1 X1358 X354 X1357 X1317 X2826 X1361 X2814 X3021 (a, b, c) = (5, 6, 7) | AB = 1

X3021 (5th STEVANOVIC POINT) 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 \(f(a,b,c) = bc(b + c - a)[2a^{2} - a(b + c) + (b - c)^{2}]^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.622145251850\)

X3021 lies on the incircle.

▸ Incident Central Lines14 lines

{1, 1358}, {11, 55}, {56, 1292}, {354, 1357}, {1317, 2826}, {1361, 2814}, {1362, 2820}, {1364, 2835}, {1682, 3034}, {2775, 3028}, {2788, 3027}, {2795, 3023}, {2809, 3022}, {2836, 3024}

▸ Functional Relations6 relations