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MathNet 2010 — Part 03 Question 133

Math Olympiad Vault · MathNet 2010 — Part 03

Question 133

The reds and greens are doing a battle in water balloons. The base of the reds is an area in the shape of an equilateral triangle of 8 meters side. Greens cannot enter the base of reds, but they can throw their bullets into the base while still being out of the perimeter. Knowing that the Greens manage to hit a target up to a maximum distance of 1 meter, how big (in square meters) is the area inside the base of the reds safe from the shooting range of the greens?
  1. $19 \sqrt{3}-24$
  2. $4 \sqrt{3}$
  3. $3 \sqrt{3}$
  4. $19-8 \sqrt{3}$
  5. Each point of the red area is within reach of the greens.