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单词 Feuerbach's Theorem
释义

Feuerbach's Theorem

1. The Circle which passes through the feet of the Perpendiculars dropped from theVertices of any Triangle on the sides opposite them passes also through theMidpoints of these sides as well as through the Midpoint of the segments which join theVertices to the point of intersection of the Perpendicular (a Nine-PointCircle).

2. The Nine-Point Circle of any Triangle is Tangent internally to the Incircle andTangent externally to the three Excircles.

See also Excircle, Feuerbach Point, Incircle, Midpoint, Nine-Point Circle, Perpendicular,Tangent


References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 117-119, 1967.

Dixon, R. Mathographics. New York: Dover, p. 59, 1991.


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更新时间:2025/2/22 21:32:02