## Task A-1.3.

Given is a triangle $A B C$ where $\varangle B A C=45^{\circ},|A B|=4,|A C|=3 \sqrt{2}$. Let $\overline{A D}$ and $\overline{B E}$ be the altitudes of this triangle. The perpendicular to $\overline{A B}$ through point $E$ intersects the segment $\overline{A D}$ at point $P$.

Determine $|E P|$.