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2019 AMC 12A Question 18

AMC12 · 2019 AMC 12A

Question 18

A sphere with center $O$ has radius $6.$ A triangle with sides of length $15,$ $15,$ and $24$ is situated in space so that each of its sides is tangent to the sphere. What is the distance between $O$ and the plane determined by the triangle?
  1. $2\sqrt{3}$
  2. $4$
  3. $3\sqrt{2}$
  4. $2\sqrt{5}$
  5. $5$