VTMO 2026 - Grade 9 - Semifinal - SET 04 - Self-study Question 1

In the coordinate plane, let $(d_1):y=ax+3$ and $(d_2):y=bx+3$. Let $A=d_1\cap d_2$, $B=d_1\cap Ox$, and $C=d_2\cap Ox$. Triangle $ABC$ is right-angled at $A$ and has a $60^\circ$ angle. Find $P=a^2+b^2$.