两圆互作切线

hbghlyj

MathWorld写道，可以从\begin{align}
d_1^2+h^2 & =h_1^2 \\
d_2^2+h^2 & =h_2^2 \\
r_1^2+\left(l_1-h_2\right)^2 & =h_1^2 \\
r_2^2+\left(l_2-h_1\right)^2 & =h_2^2 \\
d_1+d_2 & =d \\
r_1^2+l_1^2 & =d^2 \\
r_2^2+l_2^2 & =d^2 \\
s_1 h_1 & =h r_1 \\
s_2 h_2 & =h r_2
\end{align}这九个方程中，消去$ d_1, d_2, h, h_1, h_2, l_1, l_2$，这个怎样办到呢？会得到$s_1,s_2$满足相同的8次方程？

kuing

啥意思，直接由
\[\frac{s_1}{r_1}=\frac{r_2}d,~\frac{s_2}{r_2}=\frac{r_1}d\]
不就得到
\[s_1=s_2=\frac{r_1r_2}d\]
了吗？

hbghlyj

The Eyeball Theorem generalized

Praying Eyes Theorem

The Praying Eyes theorem generalized