Problem

Source: Slovenia 1997 4th Grade P3

Tags: geometry



Two disjoint circles $k_1$ and $k_2$ with centers $O_1$ and $O_2$ respectively lie on the same side of a line $p$ and touch the line at $A_1$ and $A_2$ respectively. The segment $O_1O_2$ intersects $k_1$ at $B_1$ and $k_2$ at $B_2$. Prove that $A_1B_1\perp A_2B_2$.