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angles wanted in right triangle, BC<AC, DE=AB, perp. bisector

Source: Austria Beginners' Competition 2010 p4

October 3, 2021
geometryanglesright triangle

Problem Statement

In the right-angled triangle ABCABC with a right angle at CC, the side BCBC is longer than the side ACAC. The perpendicular bisector of ABAB intersects the line BCBC at point DD and the line ACAC at point EE. The segments DEDE has the same length as the side ABAB. Find the measures of the angles of the triangle ABCABC.
(R. Henner, Vienna)
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