将任意三角形的内、外角三等分,以分别接近于三条边的内(外)角的三等分线的交点为顶点的三角形称为内(外)莫勒三角形,以分别接近于三条边的一个内角和其余两个角的外角三等分线的交点为顶点的三角形称为旁莫勒三角形.若延长内莫勒三角形的三边与组成外莫勒三角形的外角三等分线相交,则可得三个内部含有旁莫勒三角形的三角形(简称为“内含旁”莫勒三角形)及两个与其有关的不等式.本文记△ABC 的外接圆半径为 R,内切圆半径为 r,内角 A、B、C 以及它们的外角分别为 Triangularly dividing the inner and outer corners of any triangle, the triangles with vertices at the intersections of the three bisectors of the inner (outer) corners that are close to the three sides are called inner (external) Moeller triangles, respectively, close to the three sides. The triangle with the intersection of the inner corner and the outer corner bisector of the remaining two corners is called the side-mollet triangle. If the three sides of the extended Nemore triangle intersect with the outer corner trisection that makes up the outer Morole triangle, You can get three triangles that contain a side-by-Mole triangle (abbreviated as the “lateral” Moeller triangle) and two related inequalities. The circumscribed circle radius of ABC in this paper is R, and the inscribed radius For r, the inner corners A, B, C, and their outer corners are