X,Y,Z是复平面单位圆上的点，求X点的切线与YZ交点的坐标。

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1. In[]:= expr=x((2x-y-z)/(x^2-y z)-1/x);
2. (expr/.{x->1/x,y->1/y,z->1/z})+expr//Factor
3. Out[]= 0

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$$\Re\left[(x-0)\overline{(p-x)}\right]=\Re\left[x\cdot\left(\frac{2x-y-z}{x^2-y z}-\frac1x\right)\right]=0\implies \vv{PX}\perp\vv{OX}$$

1. In[]:= p=(x^2 y+x^2 z-2x y z)/(x^2-y z);
2. expr=(p-y)/(p-z);
3. (expr/.{x->1/x,y->1/y,z->1/z})-expr//Factor
4. Out[]= 0

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$$\Im\left[p-y\over p-z\right]=0\implies \vv{PY}\px\vv{PZ}$$

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