Difference between revisions of "2021 AMC 10A Problems/Problem 19"
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<math>\textbf{(A)} ~18\qquad\textbf{(B)} ~27\qquad\textbf{(C)} ~36\qquad\textbf{(D)} ~45\qquad\textbf{(E)} ~54</math> | <math>\textbf{(A)} ~18\qquad\textbf{(B)} ~27\qquad\textbf{(C)} ~36\qquad\textbf{(D)} ~45\qquad\textbf{(E)} ~54</math> | ||
| − | ==Solution== | + | == Solution 1 == |
| + | <asy> | ||
| + | size(10cm); | ||
| + | filldraw(arc((-3,0),3,180,180) -- cycle, gray); | ||
| + | filldraw(arc((0,3),3,0,180) -- cycle, gray); | ||
| + | filldraw(arc((3,0),3,180,180) -- cycle, gray); | ||
| + | filldraw(arc((0,-3),3,180,180) -- cycle, gray); | ||
| + | filldraw((-3,3)--(3,3)--(3,-3)--(-3,-3)--cycle, grey); | ||
| + | </asy> | ||
| + | |||
| + | |||
https://artofproblemsolving.com/wiki/index.php/File:Image_2021-02-11_111327.png (someone please help link file thanks) | https://artofproblemsolving.com/wiki/index.php/File:Image_2021-02-11_111327.png (someone please help link file thanks) | ||
Revision as of 17:03, 11 February 2021
Problem 19
The area of the region bounded by the graph of![\[x^2+y^2 = 3|x-y| + 3|x+y|\]](http://latex.artofproblemsolving.com/8/4/b/84b498bfa9802780599eea78d4507cbe55897db6.png)
is 
, where 
and 
are integers. What is 
?
Solution 1
![[asy] size(10cm); filldraw(arc((-3,0),3,180,180) -- cycle, gray); filldraw(arc((0,3),3,0,180) -- cycle, gray); filldraw(arc((3,0),3,180,180) -- cycle, gray); filldraw(arc((0,-3),3,180,180) -- cycle, gray); filldraw((-3,3)--(3,3)--(3,-3)--(-3,-3)--cycle, grey); [/asy]](http://latex.artofproblemsolving.com/e/e/6/ee62b203aa6bfd62e9f14f675e1d161a95a10189.png)
https://artofproblemsolving.com/wiki/index.php/File:Image_2021-02-11_111327.png (someone please help link file thanks)
Video Solution (Using absolute value properties to graph)
~ pi_is_3.14
