English: Charting a river - measuring its width at a given location using the intercept theorem.

The intercept theorem can be used to determine a distance that cannot be measured directly, such as the width of a river or a lake, the height of tall buildings or similar. The graphic to the right illustrates measuring the width of a river. The segments ${\displaystyle |CF|}$,${\displaystyle |CA|}$,${\displaystyle |FE|}$ are measured and used to compute the wanted distance ${\displaystyle |AB|={\frac {|AC||FE|}{|FC|}}}$.