Difference between revisions of "2019 AMC 8 Problems/Problem 24"

(Created page with "==Problem== ==Solution 1== ==Solution 2== {{AMC8 box|year=2019|num-b=23|num-a=25}}")
 
(Added diagram)
Line 1: Line 1:
 
==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}}

Revision as of 16:33, 20 November 2019

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 2

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions
Invalid username
Login to AoPS