Difference between revisions of "2019 AMC 8 Problems/Problem 24"
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==Problem== | ==Problem== | ||
| + | <asy> | ||
| + | unitsize(2cm); | ||
| + | pair A,B,C,DD,EE,FF; | ||
| + | B = (0,0); C = (3,0); | ||
| + | A = (1.2,1.7); | ||
| + | DD = (2/3)*A+(1/3)*C; | ||
| + | EE = (B+DD)/2; | ||
| + | FF = intersectionpoint(B--C,A--A+2*(EE-A)); | ||
| + | draw(A--B--C--cycle); | ||
| + | draw(A--FF); | ||
| + | draw(B--DD);dot(A); | ||
| + | label("$A$",A,N); | ||
| + | dot(B); | ||
| + | label("$B$", | ||
| + | B,SW);dot(C); | ||
| + | label("$C$",C,SE); | ||
| + | dot(DD); | ||
| + | label("$D$",DD,NE); | ||
| + | dot(EE); | ||
| + | label("$E$",EE,NW); | ||
| + | dot(FF); | ||
| + | label("$F$",FF,S); | ||
| + | </asy> | ||
| + | |||
==Solution 1== | ==Solution 1== | ||
==Solution 2== | ==Solution 2== | ||
{{AMC8 box|year=2019|num-b=23|num-a=25}} | {{AMC8 box|year=2019|num-b=23|num-a=25}} | ||
![[asy] unitsize(2cm); pair A,B,C,DD,EE,FF; B = (0,0); C = (3,0); A = (1.2,1.7); DD = (2/3)*A+(1/3)*C; EE = (B+DD)/2; FF = intersectionpoint(B--C,A--A+2*(EE-A)); draw(A--B--C--cycle); draw(A--FF); draw(B--DD);dot(A); label("$A$",A,N); dot(B); label("$B$", B,SW);dot(C); label("$C$",C,SE); dot(DD); label("$D$",DD,NE); dot(EE); label("$E$",EE,NW); dot(FF); label("$F$",FF,S); [/asy]](http://latex.artofproblemsolving.com/c/f/5/cf5d315e13b9e158a6df354d7f9a8ecafaf2b131.png)
