# Can I trisect your angle?

Geometry Level 4

In $$\triangle ABC$$, $$AB=4$$ and $$\angle B=45^\circ$$. Cevians $$BD$$ and $$BE$$ ($$D, E \in AC$$) divide $$\angle B$$ into three congruent angles. If $$BD$$ is a median of $$\triangle ABC$$, find $$BD^2$$.

A cevian is a segment from one vertex of the triangle to the opposite side.

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