In the following figure, prove that AB+AC>OB+OC

Dear student

Given:
In triangle ABC, O is any interior point.
We know that any segment from a point O inside a triangle to any vertex of the triangle cannot be longer than the two sides adjacent to the vertex.
Thus, OA cannot be longer than both AB and CA (if this is possible, then O is outside the triangle).

 OA cannot be longer than both AB and CA.​
$$\begin{gathered} AB>OB ...\left(1\right) \\ AC>OC ...\left(2\right) \\ \mathrm{Thus}, AB+AC>OB+OC ...[\mathrm{Adding} (1) \mathrm{and}(2\left)\right] \end{gathered}$$

Regards