X₃₀₂₂

6th STEVANOVIC POINT

X₃₀₂₂ = X₉₉-of-intouch-triangle

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

X₃₀₂₂ (6th STEVANOVIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 116}, {12, 118}

• Related Centers: X₁₁ (FEUERBACH POINT), X₁₁₆ (MIDPOINT OF X₄ AND X₁₀₃), X₁₂ ({X), X₁₁₈ (MIDPOINT OF X₄ AND X₁₀₁)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b - c)^{2}(b + c - a)^{3}\)

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

Search Value (6, 9, 13): \(2.935176009820\)

X₃₀₂₂ lies on the incircle.

▸ Incident Central Lines22 lines

{1, 1362}, {11, 116}, {12, 118}, {33, 181}, {56, 103}, {65, 1360}, {101, 2291}, {150, 497}, {152, 388}, {926, 2170}, {928, 1364}, {950, 2784}, {1282, 1697}, {1317, 2801}, {1359, 2823}, {1361, 2099}, {1397, 2192}, {1682, 3033}, {2772, 3028}, {2774, 3024}, {2786, 3023}, {2809, 3021}

▸ Functional Relations10 relations

• X₃₀₂₂ = reflection of X_i in X_j for these (i,j): (8, 3041), (1362, 1)

• X₃₀₂₂ = X_i-Ceva conjugate of X_j for these (i,j): (7, 650), (55, 657)

• X₃₀₂₂ = crosspoint of X_i and X_j for these (i,j): (7, 650), (55, 657), (607, 663)

• X₃₀₂₂ = crosssum of X_i and X_j for these (i,j): (7, 658), (55, 651), (100, 144), (279, 934), (348, 664)

• X₃₀₂₂ = X₉₉-of-intouch-triangle

• X₃₀₂₂ = X₁₀₁-of-Mandart-incircle-triangle

• X₃₀₂₂ = trilinear product of vertices of intangents triangle

• X₃₀₂₂ = trilinear product of vertices of Mandart-incircle triangle

• X₃₀₂₂ = homothetic center of intangents triangle and reflection of extangents triangle in X₁₀₁

• X₃₀₂₂ = intersection, other than vertices of intouch triangle, of incircle and Privalov conic