X₁₉₇

X₈-CEVA CONJUGATE OF X₆

X₁₉₇ = X₈-Ceva conjugate of X₆

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

X₁₉₇ (X₈-CEVA CONJUGATE OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 10}, {19, 25}

• Related Centers: X₈ (NAGEL POINT), X₆ (SYMMEDIAN POINT), X₃ (CIRCUMCENTER), X₁₀ (SPIEKER CENTER), X₁₉ (CLAWSON POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES)

Trilinears: \(a[-a^{2}\tan A/2 + b^{2}\tan B/2 + c^{2}\tan C/2] : :\)

Search Value (6, 9, 13): \(-8.822549019410\)

▸ Incident Central Lines7 lines

{3, 10}, {6, 181}, {19, 25}, {22, 100}, {42, 48}, {56, 227}, {159, 200}

▸ Functional Relations5 relations

• X₁₉₇ = X₈-Ceva conjugate of X₆

• X₁₉₇ = crosssum of X₁₂₄ and X₅₁₄

• X₁₉₇ = isogonal conjugate of X₈₀₄₈

• X₁₉₇ = crossdifference of every pair of points on line X₉₀₅X₃₉₁₀

• X₁₉₇ = crosspoint of circumcircle intercepts of excircles radical circle

Notes

Let N_aN_bN_c be the extouch triangle. Let A″ be the crosspoint of the circumcircle intercepts of line N_bN_c, and define B″, C″ cyclically. The lines N_aA″, N_bB″, N_cC″ concur in X₁₉₇. (Randy Hutson, July 31 2018)

For a construction of X₁₉₇, see Dasari Naga Vijay Krishna, “On A Simple Construction of Triangle Centers X₈, X₁₉₇, X(K) & X₅₉₄”, Scientific Inquiry and Review, Vol. 2, Issue 3, July 2018.