X₃₈₂₂

X₂₀₉₉com(3rd EULER TRIANGLE)

Suppose that ABC is an acute triangle. Let L_A be the circle that is externally tangent to the nine-point circle and to the sidelines AB and AC. Define L_B and L_C cyclically. The three circles are here named the Odehnal tritangent circles. Their radical center is X₃₈₂₂. The center of the Apollonian circle of L_A, L_B, L_C is X₆₁₆₇. (Boris Odehnal, “A Triad of Tritangent Circles, Journal for Geometry and Graphics 18 (2014) no. 1, 61-71)

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

X₃₈₂₂ (X₂₀₉₉com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {10, 12}, {2, 36}

• Related Centers: X₁₀ (SPIEKER CENTER), X₁₂ ({X), X₂ (CENTROID), X₃₆ (INVERSE-IN-CIRCUMCIRCLE OF INCENTER)

Barycentrics: \((b + c)(b^{3} + c^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} - abc) : :\)

Search Value (6, 9, 13): \(2.052750918001\)

▸ Incident Central Lines18 lines

{1, 2476}, {2, 36}, {5, 515}, {10, 12}, {11, 551}, {21, 3585}, {35, 2475}, {37, 115}, {63, 1698}, {100, 3584}, {116, 119}, {377, 498}, {381, 1001}, {495, 519}, {496, 3636}, {1329, 3634}, {1621, 3583}, {2901, 3178}