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MathNet 2020 — Math Olympiad Vault — Part 05 Question 35

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 35

Juca is a scout exploring near his campsite. After collecting fruit and wood, he must fetch water from the river and return to his tent. In the figure, Juca is represented by $J$, the river by line $r$, and his tent by $B$. The perpendicular feet $C,E$ of $B,J$ on $r$ are $180\ \mathrm{m}$ apart.

Question illustration

What is the shortest distance Juca can travel to return to his tent via the river?