[ Measurement of segment lengths and angle measures. Adjacent angles.]

On a straight line, points $A, B$, and $C$ are given. It is known that $A B=5$, and segment $A C$ is 1 unit longer than $B C$. Find $A C$ and $B C$.

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Consider all possible cases of the arrangement of points $A, B$, and $C$.

## Solution

If the point lies outside the segment $A B$, then $A C$ and $B C$ differ by 5, which contradicts the condition. Let point $C$ lie between $A$ and $B$. Then $A C + B C = A B$, or $2 B C + 1 = 5$. From this, $B C = 2, A C = 3$.

## Answer

$B C = 2, A C = 3$.