The problem statement contains contradictory information regarding the side lengths of ABC and the property that B lies on the circumference of a circle with diameter AC. If AC is the diam

The problem statement contains contradictory information regarding the side lengths of $\triangle ABC$ and the property that B lies on the circumference of a circle with diameter AC. If AC is the diameter and B is on the circumference, then $\angle ABC$ must be $90^\circ$. However, the given side lengths $AB=q$, $BC=2q$, and $AC=2q$ (from "AC = BC = 2q and AB = q") do not satisfy the Pythagorean theorem ($q^2 + (2q)^2 \neq (2q)^2$).

To resolve this, we will assume the standard properties of a triangle inscribed in a semicircle and that the side lengths are intended to form a right-angled triangle. The most common right-angled triangle involving $q