Difference between revisions of "2021 AMC 10B Problems/Problem 7"
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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 | 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 | ||
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| + | == Video Solution by OmegaLearn (Area of Circles and Logic) == | ||
| + | https://youtu.be/yPIFmrJvUxM | ||
| + | |||
| + | ~ pi_is_3.14 | ||
{{AMC10 box|year=2021|ab=B|num-b=6|num-a=8}} | {{AMC10 box|year=2021|ab=B|num-b=6|num-a=8}} | ||
Revision as of 01:55, 12 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
![[asy] /* diagram made by samrocksnature */ pair A=(10,0); pair B=(-10,0); draw(A--B); draw(circle((0,-1),1)); draw(circle((0,-3),3)); draw(circle((0,-5),5)); draw(circle((0,7),7)); dot((0,7)); draw((0,7)--(0,0)); label("$7$",(0,3.5),E); label("$l$",(-9,0),S); [/asy]](http://latex.artofproblemsolving.com/5/4/8/5481e45f8fbf33deba5c7afb818793e2e33f4269.png)
After a bit of wishful thinking and inspection, we find that the above configuration maximizes our area. 
~ samrocksnature
Video Solution by OmegaLearn (Area of Circles and Logic)
~ pi_is_3.14
| 2021 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
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| All AMC 10 Problems and Solutions | ||
