7.3. On a plane, there are points $A, B, C, D, X$. Some segment lengths are known: $A C=2$, $A X=5$, $A D=11$, $C D=9$, $C B=10$, $D B=1$, $X B=7$. Find the length of the segment $C X$.
Answer: 3.

Solution: Note that $A D=11=2+9=A C+C D$. Therefore, points $A, C, D$ lie on the same line $C D$ (since the triangle inequality becomes an equality). Note that $C B=10=9+1=C D+D B$. Therefore, points $C, D, B$ lie on the same line $C D$ (since the triangle inequality becomes an equality). Therefore, all four points lie on the same line $C D$, with $C$ between $A D$ and $D$ between $C$ and $B$, i.e., in the order $A, C, D, B$. Note that $A B=A D+D B=11+1=5+7=A X+X B$. Therefore, points $A, X, B$ lie on the same line $A B$ (since the triangle inequality becomes an equality).

Thus, all points lie on the segment $A B$. Therefore, $C X=A X-A C=5-2=3$.

## Criteria:

Answer only - 0 points.

Answer with verification - 1 point.

Solution based on the assumption that all points lie on one line - no more than 3 points.