Have You Heard Of Symmedian?

Geometry Level 4

A triangle \(ABC\) is inscribed inside a circumcircle with center \(O\). Draw the median \(AM\) of the circle. Now, draw the tangents of the circle \(O\) at \(B\) and \(C\), they cut at point \(P\). \(AP\) cuts the circle \(O\) at \(D\). If \(\angle BDM = 27^\circ\), find \(\angle AOC\) in degrees?

Clarification: For anyone who doesn't know what symmedian is, it's just the reflection of the median on bisector. For example, a triangle \(ABC\) with median \(AM\) and bisector \(AI\). If you draw the reflection \(AD\) of \(AM\) on \(AI\) then \(AD\) is symmedian.

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