Final answer:
The size of angle AOB is 90 degrees because it is formed by the radii PA and PB. The size of angle APB is also 90 degrees because it is formed by the tangent PB and the radius OB.
Step-by-step explanation:
To find the size of angle AOB, we need to use the properties of tangents and circles. Since PB and PA are tangents to circle O, they are perpendicular to radii drawn to the points of tangency. Angle AOB is formed by the radii PA and PB. In a circle, the angle formed by two radii is always 90 degrees. Therefore, angle AOB is 90 degrees.
To find the size of angle APB, we can use the fact that the angle between a tangent and a radius is 90 degrees. Angle APB is formed by the tangent PB and the radius OB. Therefore, angle APB is also 90 degrees.