Difference between revisions of "2019 AMC 8 Problems/Problem 24"
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| − | ==Problem== | + | |
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| + | ==Problem 24== | ||
| + | In triangle <math>ABC</math>, point <math>D</math> divides side <math>\overline{AC}</math> s that <math>AD</math>:<math>DC=1</math>:<math>2</math>. Let <math>E</math> be the midpoint of <math>\overline{BD}</math> and left <math>F</math> be the point of intersection of line <math>BC</math> and line <math>AE</math>. Given that the area of <math>\triangle ABC</math> is <math>360</math>, what is the area of <math>\triangle EBF</math>? | ||
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<asy> | <asy> | ||
unitsize(2cm); | unitsize(2cm); | ||
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label("$F$",FF,S); | label("$F$",FF,S); | ||
</asy> | </asy> | ||
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| + | <math>\textbf{(A) }24\qquad\textbf{(B) }30\qquad\textbf{(C) }32\qquad\textbf{(D) }36\qquad\textbf{(E) }40</math> | ||
==Solution 1== | ==Solution 1== | ||
| − | == | + | |
| − | {{AMC8 box|year=2019|num-b= | + | |
| + | ==See Also== | ||
| + | {{AMC8 box|year=2019|num-b=19|num-a=21}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Revision as of 17:37, 20 November 2019
Problem 24
In triangle 
, point 
divides side 
s that 
:
:
. Let 
be the midpoint of 
and left 
be the point of intersection of line 
and line 
. Given that the area of 
is 
, what is the area of 
?
![[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)
Solution 1
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 | ||
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