X₁₆₂₅

TCC-PERSPECTOR OF X₁₆₃

X₁₆₂₅ is the tcc-perspector of X₁₆₃.

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

X₁₆₂₅ (TCC-PERSPECTOR OF X₁₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3289, 3331}

• Related Centers: X₃₂₈₉ (INTERSECTION OF LINES X), X₃₃₃₁ (INTERSECTION OF LINES X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X₁₆₀₁)

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

Search Value (6, 9, 13): \(0.059755211132\)

X₁₆₂₅ lies on the Johnson circumconic.

▸ Incident Central Lines3 lines

{5, 217}, {6, 13}, {110, 112}

▸ Functional Relations7 relations

• X₁₆₂₅ = midpoint of X₃₂₈₉ and X₃₃₃₁

• X₁₆₂₅ = isogonal conjugate of X₁₅₄₁₂

• X₁₆₂₅ = X₇₅-Ceva conjugate of X₆

• X₁₆₂₅ = crosspoint of X_i and X_j for these (i,j): (110, 648), (107, 110)

• X₁₆₂₅ = crosssum of (523,647), (520,523)

• X₁₆₂₅ = crossdifference of every pair of points on line X₁₂₅X₅₂₆

• X₁₆₂₅ = barycentric product X₁₁₂*X₃₄₃