MathDB
Determine the angles of ABC

Source: Baltic Way 2001

November 17, 2010
geometrycircumcirclegeometry proposed

Problem Statement

In a triangle ABCABC, the bisector of ∠BAC\angle BAC meets the side BCBC at the point DD. Knowing that ∣BD∣⋅∣CD∣=∣AD∣2|BD|\cdot |CD|=|AD|^2 and ∠ADB=45∘\angle ADB=45^{\circ}, determine the angles of triangle ABCABC.
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