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MathNet 2012 Question 39

Math Olympiad Vault · MathNet 2012

Question 39

In the triangle $ABC$, $\angle ABC = 45^\circ$, $BC = 1$ and $E$ is a point on the side $AC$ such that $EC = 1$.
The line perpendicular to $AC$ through $E$ meets the line $BC$ at the point $D$ so that $CD = 2$ and $C$ is interior to $DB$.
Determine the angles of the triangle $ABD$.

Illustrative configuration only.

Question illustration