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Last edited by lihpb 2023-11-5 22:59四面体\(A_1\)\(A_2\)\(A_3\)\(A_4\)的各顶点\(A_i\)所在的高分别为\(h_i\)，\(A_i\)所对侧面的旁切球半径为\(r_i\)，\(1\le i\le4\)
求证:
\(\displaystyle\sum_{0\le i<j\le4}\)\(\dfrac{h_ih_j}{r_ir_j}\ge24\),
\(\displaystyle\sum_{0\le i<j<k\le4}\)\(\dfrac{h_ih_jh_k}{r_ir_jr_k}\ge32\),
等号成立的充要条件是四面体各侧面面积相等 |
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