VTMO 2026 - Grade 7 - Semifinal - SET 7 - Self-study Question 3

Positive integers $a,b,c,d$ satisfy $A=\frac ab+\frac cd=\frac ab\cdot\frac cd$ and $B=\frac ba+\frac dc=\frac ab\div\frac cd$. Find $A^2+B^2$.