X₁₃₆₀

BRISSE TRANSFORM OF X₁₀₃

X₁₃₆₀ = X₃₅₆₃-of-intouch triangle (Chris van Tienhoven, Hyacinthos #21096, Jul 14, 2012)

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

X₁₃₆₀ (BRISSE TRANSFORM OF X₁₀₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Intouch (Contact) Triangle △T_aT_bT_c — vertices T_a, T_b, T_c (Contact triangle of Incircle touchpoints on BC, CA, AB)

• Circle: Incircle (incircle) — Inscribed circle tangent to sidelines at T_a, T_b, T_c; centered at X₁ INCENTER

• Concurrence Lines: T_a–X₁₃₆₀, T_b–X₁₃₆₀, T_c–X₁₃₆₀ concurring at X₁₃₆₀

• Related Centers: X₁ (INCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) where f(a,b,c) is as above X₁₃₅₄, using X = X₁₀₃

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

Search Value (6, 9, 13): \(0.154258030103\)

X₁₃₆₀ lies on the incircle.

▸ Incident Central Lines5 lines

{11, 57}, {12, 208}, {55, 108}, {56, 105}, {354, 1364}

▸ Functional Relations1 relation

• X₁₃₆₀ = X₃₅₆₃-of-intouch triangle (Chris van Tienhoven, Hyacinthos #21096, Jul 14, 2012)