Jubayer's circle

Geometry Level 2

In triangle \(\triangle ABC\), \(AB = 37, AC = 33\), and \(BC = 39\). A circle \(\Gamma\) is drawn with center \(A\) and radius \(AC\). Let \(D\) be the point on \(\Gamma\) that is furthest from \(B\). What is the distance \(BD\)?

This problem is posed by Jubayer N.

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