X₃₆₁₁

2nd AYME-MOSES PERSPECTOR

In a Hyacinthos message dated January 7, 2011, Jean-Louis Ayme noted that the orthic triangle of ABC is perspective to the medial triangle of the extangents triangle of ABC. Peter Moses found coordinates for the perspector, X₃₆₁₁.

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

X₃₆₁₁ (2nd AYME-MOSES PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 51}, {40, 185}

• Related Centers: X₁₉ (CLAWSON POINT), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₄₀ (BEVAN POINT), X₁₈₅ (NAGEL POINT OF THE ORTHIC TRIANGLE)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c) (b^{2} + c^{2} - a^{2})[a^{3}(b + c) + (b - c)^{2}(b^{2} + c^{2} - a^{2} - ab - ac + 2bc)]\)

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

Search Value (6, 9, 13): \(11.445727974451\)

▸ Incident Central Lines10 lines

{19, 51}, {25, 3197}, {40, 185}, {42, 1409}, {55, 184}, {65, 225}, {71, 228}, {209, 3198}, {511, 3101}, {1899, 2550}