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fundamental theorem on isogonal lines∗
drini†
2013-03-21 14:50:01
Let 4ABC be a triangle and AX, BY, CZ three concurrent lines at P . If
AX 0 , BY 0 , CZ 0 are the respective isogonal conjugate lines for AX, BY, CZ, then
AX 0 , BY 0 , CZ 0 are also concurrent at some point P 0 .
An applications of this theorem proves the existence of Lemoine point (for
it is the intersection point of the symmedians):
This theorem is a direct consequence of Ceva’s theorem (trigonometric version).
∗ hFundamentalTheoremOnIsogonalLinesi created: h2013-03-21i by: hdrinii version:
h33407i Privacy setting: h1i hTheoremi h51-00i
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