<Cir-2024-763>, hint

Let T, T' be points of tangency, then <CTA=<CT'B=90

Let <CAT=x,  then since AT//BT', <CBT'=90-x.

Since CT=CT' (radius), AB cosA sinx=CT=CT'=AB sinA cosx

Hence tanA=tanx,<A=x. tanA=a/b. CT=b sinA