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In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is : where ''A, B, C'' denote both the triangle's vertices and the angle measures at those vertices, ''H'' is the orthocenter (the intersection of the triangle's altitudes), ''D'', ''E'', ''F'' are the feet of the altitudes from vertices ''A, B, C'' respectively, ''R'' is the triangle's circumradius (the radius of its circumscribed circle), and ''a'', ''b'', ''c'' are the lengths of the triangle's sides opposite vertices ''A'', ''B'', ''C'' respectively.〔Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publications, 2007 (orig. 1960).〕 The first parts of the radius formula reflect the fact that the orthocenter divides the altitudes into segment pairs of equal products. The trigonometric formula for the radius shows that the polar circle has a real existence only if the triangle is obtuse, so one of its angles is obtuse and hence has a negative cosine. ==Construction== The polar circle can be geometrically constructed as follows. Pick one of the vertices of the triangle, say ''A''. Let ''Z'' be the point where the altitude from ''A'' intersects the opposing side ''BC''. Now draw the line through the orthocenter perpendicular to the altitude from ''A''. There will be two points ''P'' on this line with the property that ''APZ'' is a right angle. The polar circle is the circle about the orthocenter of the triangle that passes through these two points. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Polar circle (geometry)」の詳細全文を読む スポンサード リンク
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