X₃₅₂

INVERSE-IN-CIRCUMCIRCLE OF X₃₅₃

X₃₅₂ = inverse-in-circumcircle of X₃₅₃

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

X₃₅₂ (INVERSE-IN-CIRCUMCIRCLE OF X₃₅₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {843, 187}

• Related Centers: X₈₄₃ (ISOGONAL CONJUGATE OF X₅₄₃), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(-a^{4} - b^{4} - c^{4} - 5b^{2}c^{2} + 4a^{2}b^{2} + 4a^{2}c^{2})\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-8.749665363574\)

X₃₅₂ lies on the Parry circle.

▸ Incident Central Lines5 lines

{2, 6}, {3, 353}, {23, 2502}, {110, 187}, {111, 511}

▸ Functional Relations14 relations

• X₃₅₂ = reflection of X₈₄₃ in X₁₈₇

• X₃₅₂ = isogonal conjugate of X₆₀₉₄

• X₃₅₂ = inverse-in-circumcircle of X₃₅₃

• X₃₅₂ = crossdifference of every pair of points on line X₃₇₃X₅₁₂

• X₃₅₂ = X₂₃-of-circumsymmedial-triangle

• X₃₅₂ = inverse-in-{circumcircle, nine-point circle}-inverter of X₃₈₁₅

• X₃₅₂ = orthocentroidal-to-ABC similarity image of X₁₁₁

• X₃₅₂ = 4th-Brocard-to-circumsymmedial similarity image of X₁₁₁

• X₃₅₂ = X₂₇₀₉-of-1st-Parry-triangle

• X₃₅₂ = X₈₄₃-of-2nd-Parry-triangle

• X₃₅₂ = X₁₁₀-of-3rd-Parry-triangle

• X₃₅₂ = inverse-in-Parry-isodynamic-circle of X₂₃; see X₂

• X₃₅₂ = radical trace of circumcircles of Artzt and anti-Artzt triangles

• X₃₅₂ = trilinear pole, wrt 3rd Parry triangle, of Lemoine axis