2019 AMC 8 Problems/Problem 24: Difference between revisions
Created page with "==Problem== ==Solution 1== ==Solution 2== {{AMC8 box|year=2019|num-b=23|num-a=25}}" |
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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)
