TR-MO-R1 2008 Problem 13

$C$ açısı geniş açı olan $ABC$ üçgeninde $D \in [AB]$ ve $[DC] \perp [BC]$ dir. $m(\widehat{ABC}) = \alpha$ , $m(\widehat{BCA}) = 3\alpha$ ve $|AC| - |AD| = 10$ olduğuna göre $|BD|$ kaç birimdir?

a) $10$ b) $14$ c) $18$ d) $20$ e) $22$

Official text Turkish Mathematical Olympiad, first round 2008 official paper, page 5. Quoted with source.

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