X₃₉₁₇

X₂com[INVERSE(n(TANGENTIAL TRIANGLE))]

X₃₉₁₇ = reflection of X₅₁ in X₂

5, 6, 7 3, 4, 5 Kepler Kimberling

X₃₉₁₇ (X₂com[INVERSE(n(TANGENTIAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Circumcircle (circumcircle) — Passes through vertices A, B, C; centered at X₃ CIRCUMCENTER

• Central Lines: {51, 2}

• Related Centers: X₃ (CIRCUMCENTER), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₂ (CENTROID)

Trilinears: \((\cos A) (b^{2} + c^{2}) : :\)

Barycentrics: \(a^{2}(b^{2} + c^{2})(b^{2} + c^{2} - a^{2}) : :\)

Search Value (6, 9, 13): \(5.138112002270\)

▸ Alternate Coordinates2 forms

• Trilinears: \(2 b c - a b \cos B - a c \cos C : :\)

• Trilinears: \(\cot A \sin(A + \omega ) : :\)

▸ Incident Central Lines43 lines

{2, 51}, {3, 49}, {22, 1495}, {25, 1350}, {38, 1401}, {39, 3051}, {52, 140}, {63, 295}, {69, 305}, {125, 343}, {141, 427}, {143, 632}, {165, 2807}, {181, 750}, {182, 1993}, {187, 1501}, {212, 1364}, {216, 3289}, {219, 1473}, {228, 1818}, {354, 674}, {389, 631}, {404, 970}, {418, 2972}, {426, 577}, {549, 1154}, {575, 1994}, {599, 1853}, {612, 1469}, {614, 3056}, {626, 2450}, {748, 3271}, {851, 1764}, {991, 1011}, {1038, 1425}, {1040, 3270}, {1194, 1613}, {1196, 3231}, {1352, 1370}, {1915, 2076}, {2810, 3681}, {2896, 3491}, {3525, 3567}

▸ Functional Relations10 relations

• X₃₉₁₇ = isogonal conjugate of X₃₂₀₈₅

• X₃₉₁₇ = reflection of X₅₁ in X₂

• X₃₉₁₇ = crosspoint of X₃ and X₆₉

• X₃₉₁₇ = cevapoint of X₃ and X₂₂₁₃₈

• X₃₉₁₇ = complement of X₃₀₆₀

• X₃₉₁₇ = crosssum of X_i and X_j for these (i,j): {2, 7754}, {4, 25}, {6620, 9755}, {18101, 18108}

• X₃₉₁₇ = anticomplement of X₅₉₄₃

• X₃₉₁₇ = {X₂,X₅₁}-harmonic conjugate of X₃₇₃

• X₃₉₁₇ = crossdifference of every pair of points on line X₄₁₉X₂₅₀₁ (radical axis of circumcircle and orthosymmedial circle)

• X₃₉₁₇ = centroid of pedal triangle of X₂₀