This problem contains contradictory information, which makes it impossible to solve as stated.
Here's why:
- The problem states "AC is the diameter of the circle with centre O". A fundamental theorem in geometry states that the angle subtended by a diameter at any point on the circumference is a right angle. Therefore, ∠ABC must be 90∘.
- The problem also states "AC=BC=2q and AB=q". The handwritten notes on the diagram interpret 2q=8 and q=4, leading to AC=8, BC=8, and AB=4.
- If △ABC is a right-angled triangle at B (due to AC