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Last edited by hbghlyj at 2025-3-8 04:29:09四面体的各个侧面三角形为 $S_i(i=1,2,3,4)$，$S_i$ 的旁切圆半径为 $\rho_i$，旁切球半径为 $r_i$，内切球半径为 $r$
\[
S=S_1+S_2+S_3+S_4
\]
则
\[
\sum_{i=1}^4 \frac{\rho_i^2}{r_i^2} \geq 2
\]
\[
\frac{r}{\rho_i} \leq \sqrt{\frac{S-2 S_i}{S}} \leq \frac{\rho_i}{r_i}
\]
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