I am stuck on the first part. Here is what I have done so far. First I resolved $P$ into $P\sin\theta$ and $P\cos$$\theta$. Then resolving in the horizontal plane, I obtained $F_a + P$$\cos\theta=N_b$. Then resolving vertically I obtained $P\sin\theta$ + $F_b + N_a= W$. And using the information given I obtained $2F_a=N_a$ and $2F_b=N_b$. I know I need another equation to reduce the number of variables, but i'm not quite sure how to obtain that. I tried taking moments about $A$ but wasn't able to find the perpendicular distance between $A$ and the lines of action of $P$. How do I proceed?
Compute the moments around the middle of the disc (Center of mass). The normal Forces of wall A and B will give no contribution to the resulting Moment because both lines of Action passing through the Center of mass. You will have the equation for disc radius $r$ (is the sign correct?) $F_a r + F_b r - P r = 0$ and the radius cancels out. Then you can solve a System of equations to obtain $P$.