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angle wanted, bisector AD=\sqrt{BD xCD}, <ADB = 45^o

Source: 2009 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

April 28, 2021
geometryanglesangle bisectorUkraine Correspondence

Problem Statement

In triangle ABCABC, the length of the angle bisector ADAD is BD⋅CD\sqrt{BD \cdot CD}. Find the angles of the triangle ABCABC, if ∠ADB=45o\angle ADB = 45^o.
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