X₆₂₅

MIDPOINT OF X₆₂₃ AND X₆₂₄

X₆₂₅ is the midpoint of X₆₂₃ and X₆₂₄.

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

X₆₂₅ (MIDPOINT OF X₆₂₃ AND X₆₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {623, 624}

• Related Centers: X₆₂₃ (COMPLEMENT OF X₁₅), X₆₂₄ (COMPLEMENT OF X₁₆)

Trilinears: \([2(b^{4} + c^{4} - b^{2}c^{2}) - a^{2}(b^{2} + c^{2})]/a : :\)

Search Value (6, 9, 13): \(4.864495057529\)

▸ Incident Central Lines6 lines

{2, 187}, {5, 141}, {30, 620}, {115, 325}, {126, 858}, {230, 754}

▸ Functional Relations6 relations

• X₆₂₅ = midpoint of X_i and X_j for these (i,j): (115, 325), (187, 316), (623, 624)

• X₆₂₅ = isotomic conjugate of isogonal conjugate of X₂₀₉₇₇

• X₆₂₅ = polar conjugate of isogonal conjugate of X₂₂₀₈₇

• X₆₂₅ = inverse-in-nine-point-circle of X₁₄₁

• X₆₂₅ = complement of X₁₈₇

• X₆₂₅ = complementary conjugate of X₂₄₈₂

Notes

A construction of X₆₂₅ is given at Hyacinthos 27519. (Antreas Hatzipolakis and Peter Moses, April 16, 2018)