我们知道:三角形的内心,外心,重心,垂心等都有其独特的性质,这里,我们将介绍一个三角形外心与垂心相互联系的等式。即定理:三角形任一顶点至垂心的距离,等于外心至对边距离的二倍。已知H是△ABC的垂心,O是外心,OD⊥BC于D,OE⊥AC于E,OF⊥AB于F, 求证:AH=2OD,BH=2OE,CH=2OF。证明:分两种情况讨论 We know that the inner, outer heart, the center of gravity, and the vertical heart of a triangle all have their own unique characteristics. Here, we will introduce an equation in which the triangle heart and the heart are interconnected. That is, the theorem: The distance from any vertex of a triangle to the vertical center is equal to twice the distance from the outer center to the opposite side. It is known that H is the vertigo of △ABC, O is the heart, OD ⊥BC is in D, OE⊥AC is in E, and OF⊥AB is in F. Proof: AH=2OD, BH=2OE, CH=2OF. Proof: Discussion in two situations