# ICTM State 2015 Question 19

Geometry Level 4

In the diagraam shown, $$B$$ lies on $$\overline{AC}$$, $$AB=12, BC=12, \angle ADB = 15^\circ$$ and $$\angle BDC = 30^\circ$$.

If the length of $$AD$$ can be expressed as $$k + w \sqrt f$$, where $$k,w$$ and $$f$$ are positive integers with $$f$$ square-free, find $$k+w+f$$.

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