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Problem 191: (2016 AMC 10a, 21, 12a 15)
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 $PQR$? $\textbf{(A) } 0\qquad$ $ \textbf{(B) } \sqrt{6}/3\qquad$ $\textbf{(C) } 1\qquad$ $\textbf{(D) } \sqrt{6}-\sqrt{2}\qquad$ $\textbf{(E) }\sqrt{6}/2$
Solution
Exercise 191: Solution
Circles with centers $P, Q$ and $R$, having radii $1, 3$ and $5$, 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 $PQR$?
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