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2023 SSMO Team Round Problems/Problem 8

Revision as of 22:25, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Three rabbits run away from the origin at the same speed and constant velocity such that the angle between any two rabbits' directions is <math>120^\circ</math>. A...")
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Problem

Three rabbits run away from the origin at the same speed and constant velocity such that the angle between any two rabbits' directions is $120^\circ$. After $12$ seconds, a hunter with a speed $\sqrt{7}$ times that of the rabbits runs from the origin. Let the minimal time in seconds needed for her to meet (and subsequently) catch all three rabbits be $a + b\sqrt{c}$. Find $a + b + c$.

Solution

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