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AMC12 2018b Test Paper
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Sample Question 25:

Circles ω1\omega_1, ω2\omega_2, and ω3\omega_3 each have radius 44 and are placed in the plane so that each circle is externally tangent to the other two. Points P1P_1, P2P_2, and P3P_3 lie on ω1\omega_1, ω2\omega_2, and ω3\omega_3 respectively such that P1P2=P2P3=P3P1P_1P_2=P_2P_3=P_3P_1 and line PiPi+1P_iP_{i+1} is tangent to ωi\omega_i for each i=1,2,3i=1,2,3, where P4=P1P_4 = P_1. See the figure below. The area of P1P2P3\triangle P_1P_2P_3 can be written in the form a+b\sqrt{a}+\sqrt{b} for positive integers aa and bb. What is a+ba+b?

(A) 546(B) 548(C) 550(D) 552(E) 554\textbf{(A) }546\qquad\textbf{(B) }548\qquad\textbf{(C) }550\qquad\textbf{(D) }552\qquad\textbf{(E) }554




Answer Keys

Question 25: D