Trigonometry unequal bisector region, find intersection

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I am kinda confused and would appreciate help. I have two lines intersecting. Angle a is known and as well b and c. I am looking for P1 and P2

I am not sure what to search for online, I found bisect, but this is only if b and c would be equal length and even then I am not sure if this will help me.

Any Ideas from the big minds? enter image description here