二次曲线蝴蝶定理的疑问的推广的疑问

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二次曲线蝴蝶定理的疑问 的推广

如何证明？

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2N-Wing Butterfly Theorem……太繁瑣了啊

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引理、

Let in ΔRST, RU be a cevian through vertex R. Introduce angles a = ∠SRU and b = ∠URT. Then
        sin(a + b)/RU = sin(a)/RT + sin(b)/RS.

The proof is a two-liner that follows from the identity Area( ΔRST) = Area( ΔRSU) + Area( ΔRUT).

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用引理，把$\frac{1}{\mathrm{AI}}+\frac{1}{\mathrm{AJ}}+\frac{1}{\mathrm{AF}}-\left(\frac{1}{\mathrm{AK}}+\frac{1}{\mathrm{AL}}+\frac{1}{\mathrm{AM}}\right)$表示成AB,AC上的线段的倒数和，就能都消掉，为0