X₁₅₀₆

INSIMILICENTER OF MOSES AND NINE-POINT CIRCLES

X₁₅₀₆ is the insimilicenter of moses and nine-point circles.

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

X₁₅₀₆ (INSIMILICENTER OF MOSES AND NINE-POINT CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Medial Triangle △M_aM_bM_c — vertices M_a, M_b, M_c (Formed by the midpoints of sides BC, CA, AB)

• Central Lines: {2, 1078}

• Related Centers: X₂ (CENTROID), X₁₀₇₈ (INTERSECTION OF LINES X)

Trilinears: \(bc[(b^{2} - c^{2})^{2} - 2a^{2}(b^{2} + c^{2})] : :\)

Search Value (6, 9, 13): \(1.278088075568\)

▸ Linear Combinations1 combination

• X₁₅₀₆ = \(2(\tan \omega \sin 2\omega )\) X₅ + X₃₉

▸ Incident Central Lines12 lines

{2, 32}, {4, 574}, {5, 39}, {6, 17}, {11, 1500}, {12, 1015}, {51, 211}, {125, 217}, {140, 187}, {384, 620}, {485, 1505}, {486, 1504}

▸ Functional Relations4 relations

• X₁₅₀₆ = internal center of similitude of the Moses circle and the nine-point circle. [The external center is X₁₁₅; see X₁₅₀₀; Peter J. C. Moses, 6/2/03.]

• X₁₅₀₆ = complement of X₁₀₇₈

• X₁₅₀₆ = {X₆,X₁₆₅₆}-harmonic conjugate of X₇₇₄₆

• X₁₅₀₆ = {X₅,X₃₉}-harmonic conjugate of X₁₁₅