Nine-point circle
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Also known as Euler's circle. The midpoints of each side of a triangle, the feet of the three perpendicular lines drawn from each vertex to the opposite side, and the midpoints of the line segments connecting each vertex and the orthocenter are all on the same circumference (Euler proved this). This circle is called a nine-point circle. The nine-point circle is tangent to the incircle (incenter) and circumcircle (excenter) of the triangle (Feuerbach's theorem). Source : Heibonsha Encyclopedia About MyPedia Information |
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オイラーの円とも。一つの三角形の各辺の中点，各頂点から対辺に下した三つの垂線の足，各頂点と垂心を結ぶ線分の中点は同一円周上にある（オイラーが証明）。この円を九点円という。九点円はその三角形の内接円（内心）と傍接円（傍心）に接する（フォイエルバハの定理）。
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