The 3rd & 4th Moses intersection are the intersections of the Euler line with the incircle. The baristic coordinates of X₁₃₁₄, the third Moses intersection are P: (p₁ : p₂ : p₃) with p₁ = [d² + (4r - R)R + sqrt(Q)]S_BS_C + (d² + 2r² - R²)a²S_A p₂ = [d² + (4r - R)R + sqrt(Q)]S_CS_A + (d² + 2r² - R²)b²S_B p₂ = [d² + (4r - R)R + sqrt(Q)]S_AS_B + (d² + 2r² - R²)c²S_C in which: Q = 4d²R(4r - R) + [d² - 3R² + 4r(r + R)]², d = distance between the circumcenter X(3) and the orthocenter X(4), R = circumradius and r = inradius, S_A = (b² + c² - a²)/2, and S_B and S_C are defined cyclically The baristic coordinates of X₁₃₁₅, the fourth Moses intersection are P: (p₁ : p₂ : p₃) with p₁ = [d² + (4r - R)R - sqrt(Q)]S_BS_C + (d² + 2r² - R²)a²S_A p₂ = [d² + (4r - R)R - sqrt(Q)]S_CS_A + (d² + 2r² - R²)b²S_B p₂ = [d² + (4r - R)R - sqrt(Q)]S_AS_B + (d² + 2r² - R²)c²S_C

Het 3rd & 4th snijpunt van Moses zijn de snijpunten van de rechte van Euler met de ingeschreven cirkel. De baristische coördinaten van X₁₃₁₄, het derde snijpunt van Moses zijn P: (p₁ : p₂ : p₃) met p₁ = [d² + (4r - R)R + sqrt(Q)]S_BS_C + (d² + 2r² - R²)a²S_A p₂ = [d² + (4r - R)R + sqrt(Q)]S_CS_A + (d² + 2r² - R²)b²S_B p₂ = [d² + (4r - R)R + sqrt(Q)]S_AS_B + (d² + 2r² - R²)c²S_C waarin: Q = 4d²R(4r - R) + [d² - 3R² + 4r(r + R)]², d = afstand tussen het zwaartepunt X(3) en het hoogtepunt X(4), R = straal van omgeschreven cirkel and r = straal van ingeschreven cirkel, S_A = (b² + c² - a²)/2 en S_B en S_C bereken je analoog De baristische coördinaten van X₁₃₁₅, het vierde snijpunt van Moses zijn P: (p₁ : p₂ : p₃) met p₁ = [d² + (4r - R)R - sqrt(Q)]S_BS_C + (d² + 2r² - R²)a²S_A p₂ = [d² + (4r - R)R - sqrt(Q)]S_CS_A + (d² + 2r² - R²)b²S_B p₂ = [d² + (4r - R)R - sqrt(Q)]S_AS_B + (d² + 2r² - R²)c²S_C