Difference between revisions of "2019 AMC 8 Problems/Problem 24"
(Added full problem) |
(Fixed LaTeX) |
||
| Line 3: | Line 3: | ||
==Problem 24== | ==Problem 24== | ||
| − | In triangle <math>ABC</math>, point <math>D</math> divides side <math>\overline{AC}</math> s that <math>AD | + | In triangle <math>ABC</math>, point <math>D</math> divides side <math>\overline{AC}</math> s that <math>AD:DC=1:2</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>? |
<asy> | <asy> | ||
Revision as of 16:38, 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
