Have You Heard Of Symmedian?

Geometry Level 4

A triangle ABCABC is inscribed inside a circumcircle with center OO. Draw the median AMAM of the circle. Now, draw the tangents of the circle OO at BB and CC, and they cut at point PP. APAP cuts the circle OO at DD. If BDM=27\angle BDM = 27^\circ, find AOC\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, for triangle ABCABC with median AMAM and bisector AI,AI, if you draw the reflection ADAD of AMAM on AI,AI, then ADAD is the symmedian.

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