Track / Stage 4 / 257 of 340 #517 of 1964

3.10. Two circles intersect at points $A$ and $B$; $M N$ is a common tangent to them. Prove that the line $A B$ bisects the segment $M N$.

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Official solution

3.10. Let $O$ be the point of intersection of the line $A B$ and the segment $M N$. Then $O M^{2}=$ $=O A \cdot O B=O N^{2}$, i.e., $O M=O N$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.