X₂₀₇₂

INVERSE-IN-CIRCUMCIRCLE OF X₂₆

X₂₀₇₂ = complement of X₁₈₆

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

X₂₀₇₂ (INVERSE-IN-CIRCUMCIRCLE OF X₂₆) 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: {3, 26}, {2, 3} (Euler line)

• Related Centers: X₃ (CIRCUMCENTER), X₂₆ (CIRCUMCENTER OF THE TANGENTIAL TRIANGLE), X₂ (CENTROID)

Trilinears: \((J^{2} + 1) \cos A + 2(J^{2} - 1) \cos B \cos C : :\), where J is as at X₁₁₁₃

Barycentrics: \((a^{2} - b^{2} - c^{2}) (a^{6} (b^{2} + c^{2}) - a^{4} (b^{4} + c^{4}) - a^{2} (b^{2} - c^{2})^{2} (b^{2} + c^{2}) + (b^{2} - c^{2})^{4}) : :\)

Search Value (6, 9, 13): \(2.192193310314\)

▸ Incident Central Lines5 lines

{2, 3}, {125, 1568}, {127, 625}, {325, 339}, {842, 1286}

▸ Functional Relations16 relations

• X₂₀₇₂ = midpoint of X_i and X_j for these (i,j): (4, 2071), (125, 1568), (403, 858)

• X₂₀₇₂ = reflection of X_i in X_j for these (i,j): (403, 5), (2070, 468)

• X₂₀₇₂ = isogonal conjugate of X₃₈₅₃₄

• X₂₀₇₂ = complement of X₁₈₆

• X₂₀₇₂ = complementary conjugate of X₁₅₁₁

• X₂₀₇₂ = crosssum of X_i and X_j for these {i,j}: {6, 34397}, {184, 3003}

• X₂₀₇₂ = crosspoint of X_i and X_j for these {i,j}: {2, 328}, {264, 2986}

• X₂₀₇₂ = circumcircle-inverse of X₂₆

• X₂₀₇₂ = nine-point-circle-inverse of X₃

• X₂₀₇₂ = crosspoint of X₂ and X₃₂₈

• X₂₀₇₂ = center of inverse-in-nine-point-circle-of-orthocentroidal-circle

• X₂₀₇₂ = crossdifference of every pair of points on line X₅₇₁X₆₄₇

• X₂₀₇₂ = inverse-in-polar-circle of X₂₄

• X₂₀₇₂ = inverse-in-complement-of-polar-circle of X₁₄₀

• X₂₀₇₂ = inverse-in-{circumcircle, nine-point circle}-inverter of X₂₂

• X₂₀₇₂ = inverse-in-first-Droz-Farny-circle of X₃

Notes

As a point on the Euler line, X₂₀₇₂ has Shinagawa coefficients \((J^{2} + 1, J^{2} - 3)\).