Difference between revisions of "2021 AMC 10B Problems/Problem 7"
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<math>\textbf{(A) }24\pi \qquad \textbf{(B) }32\pi \qquad \textbf{(C) }64\pi \qquad \textbf{(D) }65\pi \qquad \textbf{(E) }84\pi</math> | <math>\textbf{(A) }24\pi \qquad \textbf{(B) }32\pi \qquad \textbf{(C) }64\pi \qquad \textbf{(D) }65\pi \qquad \textbf{(E) }84\pi</math> | ||
==Solution== | ==Solution== | ||
− | + | <asy> | |
+ | /* diagram made by samrocksnature */ | ||
pair A=(10,0); | pair A=(10,0); | ||
pair B=(-10,0); | pair B=(-10,0); | ||
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dot((0,7)); | dot((0,7)); | ||
draw((0,7)--(0,0)); | draw((0,7)--(0,0)); | ||
− | label(" | + | label("$7$",(0,3.5),E); |
− | label(" | + | label("$l$",(-9,0),S); |
− | + | </asy> | |
− | After a bit of wishful thinking and inspection, we find that the above configuration maximizes our area. <math>49 \pi + (25-9) \pi=65 \pi \rightarrow \boxed{D}</math> | + | After a bit of wishful thinking and inspection, we find that the above configuration maximizes our area. <math>49 \pi + (25-9) \pi=65 \pi \rightarrow \boxed{D}</math> ~ samrocksnature |
Revision as of 18:53, 11 February 2021
Problem
In a plane, four circles with radii and are tangent to line at the same point but they may be on either side of . Region consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region ?
Solution
After a bit of wishful thinking and inspection, we find that the above configuration maximizes our area. ~ samrocksnature