X₁₆₈₈

EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE)

X₁₆₈₈ is the exsimilicenter(1st Lemoine circle, 2nd Lemoine circle).

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

X₁₆₈₈ (EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1687, 1691}

• Related Centers: X₁₆₈₇ (INSIMILICENTER), X₁₆₉₁ (RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE)

Trilinears: \(\cos(A - \omega ) - \sin A : :\)

Tripolars: \(b c \sqrt{b^{2} + c^{2}} : :\)

Search Value (6, 9, 13): \(-3.902573191007\)

▸ Alternate Coordinates4 forms

• Trilinears: \(\cos A - (\sec \omega - \tan \omega ) \sin A\)

• Trilinears: \(\cos(A - \omega /2 + \pi /4) : :\)

• Trilinears: \(\sin(A - \omega /2 - \pi /4) : :\)

• Trilinears: \(\cos A - \sin(A - \omega ) : :\)

▸ Incident Central Lines11 lines

{3, 6}, {83, 2009}, {98, 2010}, {485, 1676}, {486, 1677}, {1124, 1672}, {1335, 1673}, {1377, 1680}, {1378, 1681}, {1700, 1702}, {1701, 1703}

▸ Functional Relations8 relations

• X₁₆₈₈ = reflection of X₁₆₈₇ in X₁₆₉₁

• X₁₆₈₈ = isogonal conjugate of X₂₀₁₀

• X₁₆₈₈ = circumcircle-inverse of X₁₆₈₇

• X₁₆₈₈ = Brocard-circle-inverse of X₁₆₈₉

• X₁₆₈₈ = 1st-Lemoine-circle-inverse of X₁₆₈₇

• X₁₆₈₈ = X₉₈-Ceva conjugate of X₁₆₈₇

• X₁₆₈₈ = {X₃₇₁,X₃₇₂}-harmonic conjugate of X₁₆₈₉

• X₁₆₈₈ = exsimilicenter of 2nd Brocard circle and circle {{X₃₇₁,X₃₇₂,PU(1),PU(39)}}; the insimilicenter is X₁₆₈₇