“正三角形内任一点到三边的距离之和为定值”,这是一个为大家熟知的结论.它的证明不难且有多种方法.下面用面积法来证: 如图1,点P是边长为a 的正△ABC内任意一点,记P到BC、CA、AB 边的距离分别为h1,h2,h3,则h1+h2+h2=_.(三角形高为h). 证连结PA、PB、PC有 即, “The sum of distances from any point to three sides in a regular triangle is a fixed value.” This is a well-known conclusion. Its proof is not difficult and there are multiple methods. The following area method is used to prove: Figure 1, point P is an arbitrary point within the positive △ABC with side length a, and the distance from P to BC, CA, and AB sides is h1, h2, h3, respectively, then h1+h2+h2=_. (the triangle height is h). Link PA, PB, PC there,