AB is a diameter of a circle and P is a point on the circle…

Step 1. The right angle. $\angle APB = 90^\circ$, the angle in a semicircle.

Step 2. Part (a). $\angle PBA = 180^\circ - 90^\circ - 35^\circ = 55^\circ$.

Step 3. Part (b). In the right triangle $APB$, the hypotenuse is $AB = 20\ \text{cm}$. So $PB^2 = 20^2 - 12^2 = 256$ and $PB = 16\ \text{cm}$.