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2016 AMC 10A Question 21

AMC10 · 2016 AMC 10A

Question 21

Circles with centers $P,$ $Q$ and $R,$ having radii $1,$ $2$ and $3,$ respectively, lie on the same side of line $l$ and are tangent to $l$ at $P',$ $Q'$ and $R',$ respectively, with $Q'$ between $P'$ and $R'.$ The circle with center $Q$ is externally tangent to each of the other two circles. What is the area of $\triangle PQR?$
  1. $0$
  2. $\sqrt{\dfrac{2}{3}}$
  3. $1$
  4. $\sqrt{6}-\sqrt{2}$
  5. $\sqrt{\dfrac{3}{2}}$