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单词 FundamentalTheoremOnIsogonalLines
释义

fundamental theorem on isogonal lines


Let ABC be a triangleMathworldPlanetmath and AX,BY,CZ three concurrent lines at P.If AX,BY,CZ are the respective isogonal conjugateMathworldPlanetmath lines for AX,BY,CZ, then AX,BY,CZ are also concurrentMathworldPlanetmath at some point P.

An applications of this theorem proves the existence of Lemoine point (for it is the intersectionMathworldPlanetmath point of the symmediansMathworldPlanetmath):

This theorem is a direct consequence of Ceva’s theorem (trigonometric version).

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更新时间:2025/5/4 13:02:35