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MathNet 2025 — 50 problems with figures (EN–VI) Question 27

Math Olympiad Vault · MathNet 2025 — 50 problems with figures (EN–VI)

Question 27

According to a message sent by extraterrestrial creatures who are millions of years ahead of us in development, the height of the highest two places of their planet, measured from the sea level, is $h$, whereas the lowest point on mainland has height $l$ (where $h \ge 0 \ge l$). The radius of the planet (i.e., the distance of the sea level from the centre of the planet) is $r$. Express the largest enabled by these conditions distance between two points on this planet, one of which can be visible from the other one.