<Cir-2026-796>, hint

Let XTY be tangent to both circles

<ATX=W=<ABT, <PTX=Z=<PCT (TB cuts small circle at C), <ATP=V, Z=W+V

<PCT=<PTX=W+V, Hence <BPC=<PCT-<PBC=W+V-W=V, which is <PTC( ATB is tangent  to

circle TPC). Hence <ATP=<PTC=V.