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Method B+

Here, as in the previous diagram (M-B), AD bisects the angle at A. Is D the midpoint of BC?

We can use the similar triangles ABE and ACF, and then BDE and CDF, to relate AB and AC to BD and CD.

We leave it to the reader to derive (and prove) the relationship.

You might also like to explore an alternative proof which involves constructing a triangle ACX,
where X is on BA produced and CX is parallel to DA.