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

## Problem 24

In triangle $ABC$, point $D$ divides side $\overline{AC}$ s that $AD:DC=1:2$. Let $E$ be the midpoint of $\overline{BD}$ and left $F$ be the point of intersection of line $BC$ and line $AE$. Given that the area of $\triangle ABC$ is $360$, what is the area of $\triangle EBF$?

$[asy] unitsize(2cm); pair A,B,C,DD,EE,FF; B = (0,0); C = (3,0); A = (1.2,1.7); DD = (2/3)*A+(1/3)*C; EE = (B+DD)/2; FF = intersectionpoint(B--C,A--A+2*(EE-A)); draw(A--B--C--cycle); draw(A--FF); draw(B--DD);dot(A); label("A",A,N); dot(B); label("B", B,SW);dot(C); label("C",C,SE); dot(DD); label("D",DD,NE); dot(EE); label("E",EE,NW); dot(FF); label("F",FF,S); [/asy]$

$\textbf{(A) }24\qquad\textbf{(B) }30\qquad\textbf{(C) }32\qquad\textbf{(D) }36\qquad\textbf{(E) }40$