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MathNet 2010 — Part 01 Question 60

Math Olympiad Vault · MathNet 2010 — Part 01

Question 60

Let $ABC$ be a right-angled triangle with the right angle at $C$ such that the side $BC$ is longer than the side $AC$. The perpendicular bisector of $AB$ intersects the line $BC$ in $D$ and the line $AC$ in $E$. We assume that $DE$ and the side $AB$ have the same length.

Determine the angles of the triangle $ABC$.