Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, Barrow''s inequality states the following: Let P be a point inside the triangle ABC, U, V, and W be the points where the angle bisectors of BPC, CPA, and APB intersect the sides BC, CA, AB, respectively. A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space).