Difference between revisions of "2018 AMC 8 Problems/Problem 20"
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<math>\textbf{(A) } \frac{4}{9} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } \frac{5}{9} \qquad \textbf{(D) } \frac{3}{5} \qquad \textbf{(E) } \frac{2}{3}</math> | <math>\textbf{(A) } \frac{4}{9} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } \frac{5}{9} \qquad \textbf{(D) } \frac{3}{5} \qquad \textbf{(E) } \frac{2}{3}</math> | ||
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| + | ==Solution== | ||
| + | |||
| + | Looking at this, we notice some simmilar triangles. Since <math>\line{FE}</math> | ||
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{{AMC8 box|year=2018|num-b=19|num-a=21}} | {{AMC8 box|year=2018|num-b=19|num-a=21}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:52, 21 November 2018
Problem 20
In 
a point 
is on 
with 
and 
Point 
is on 
so that 
and point 
is on 
so that 
What is the ratio of the area of 
to the area of 
![[asy] size(7cm); pair A,B,C,DD,EE,FF; A = (0,0); B = (3,0); C = (0.5,2.5); EE = (1,0); DD = intersectionpoint(A--C,EE--EE+(C-B)); FF = intersectionpoint(B--C,EE--EE+(C-A)); draw(A--B--C--A--DD--EE--FF,black+1bp); label("$A$",A,S); label("$B$",B,S); label("$C$",C,N); label("$D$",DD,W); label("$E$",EE,S); label("$F$",FF,NE); label("$1$",(A+EE)/2,S); label("$2$",(EE+B)/2,S); [/asy]](http://latex.artofproblemsolving.com/0/5/7/0571cfd5e8f21ce8031af38df8ba2295bdf2449a.png)
Solution
Looking at this, we notice some simmilar triangles. Since $\line{FE}$ (Error compiling LaTeX. Unknown error_msg)
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
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| All AJHSME/AMC 8 Problems and Solutions | ||
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