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2021 AMC 12A Question 20

AMC12 · 2021 AMC 12A

Question 20

Suppose that on a parabola with vertex $V$ and a focus $F$ there exists a point $A$ such that $AF = 20$ and $AV = 21.$ What is the sum of all possible values of the length $FV?$
  1. $13$
  2. $\dfrac{40}{3}$
  3. $\dfrac{41}{3}$
  4. $14$
  5. $\dfrac{43}{3}$