MathNet 2001 — Part 01 Question 9

In a triangle $A B C$, the bisector of $\angle B A C$ meets the side $B C$ at the point $D$. Knowing that $|B D| \cdot |C D| = |A D|^{2}$ and $\angle A D B = 45^{\circ}$, determine the angles of triangle $A B C$.