Inequality for two triangles with the same base

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Take 2 triangles, $ABC$ and $OBC$, with the same base $BC$.

If $\angle A<\angle O$, then $AB+AC>OB+OC$.

This question is derived from the textbook question - for a point $O$ in the triangle $ABC$, $AB + AC > OB + OC$.

The textbook question has been solved, and the one I asked is just a more general case. Intuitively it holds, but can anyone prove it arithmetically?

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It's not true as the picture show