Question 150
Let $\theta$ be a fixed angle. Let two circles touch each other internally at point $A$. Let $AB$ be a chord of the outer circle and such that $AB$ is not a diameter. Let $M$ be a variable point on the major arc $AB$ of the outer circle. $MA$ meets the inner circle at $N$. $P$ is a point on the segment $MB$ such that $\angle MPN = \theta$. Determine the locus of $P$ while $M$ varies.