以三角形三条高的垂足为顶点的三角形称为垂足三角形.如图,锐角△ABC,AD⊥BC,BE⊥CA,CF⊥AB,垂足分别为D、E、F,记BC=a,CA=b,AB=c,EF=a1,FD=b1,DE=c1,△ABC的面积、外接圆半径、内切圆半径、半周长分别为△、R、r和s,△DEF外接圆半径、内切圆半径、半周长分别为R1、r1和s1.设△AEF,△BDF,△CDE的面积分别为△A,△B,△C,外接圆半径、内切圆半径分别为RA,RB,RC、rA,rB,rC. Triangular triangle with three vertical feet as the vertex triangle .As shown, acute angle △ ABC, AD ⊥ BC, BE ⊥ CA, CF ⊥ AB, D, E, F respectively, note BC = a , CA = b, AB = c, EF = a1, FD = b1, DE = c1, △ ABC area, circumcircle radius, inscribed circle radius, semi-circumference were △ R, r and s, △ DEF external The radius of the circle, the radius of the inscribed circle, the radius of the inscribed circle and the radius of the inscribed circle are respectively R1, r1 and s1. The areas of △ AEF, △ BDF and △ CDE are △ A, △ B and △ C, RA, RB, RC, rA, rB, rC.