Hi guys again. I drew a diagram for this question, and I get 75 degrees for ABQ, after some shuffling of angles/ etc. I used Euclid III.32, to get to the solution as the tangent and the radius is 90 degrees, but there since PBT is 75 degrees I thought that ABQ is also 75 degrees.

However my diagram is a mess of lines and I still am not sure if the answer is 15 degrees? or 75 or something else. Although on my diagram it looks like 15, but you can never rely on diagrams

I was hoping for a clear explanation. Thanks to all!

Two circles C1 and C2 meet at the points A and B. P is a point on the circumference of C1 such that PA is tangent to C2 at A. Q is a point on the circumference of C2 outside C1. QA is produced to meet C1 again at T

so that anglePBT = 75 degrees. Find the size of angleABQ.