Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2018 AIME I Problems/Problem 4"

(→‎Solution 1)
(→‎Solution 1)
Line 10: Line 10:
 
dotfactor=3;
 
dotfactor=3;
  
−
pair B = (0,0), pair A = (6,8), pair C = (12,0)
+
pair B = (0,0), A = (6,8), C = (12,0);
 +
 
 +
label("<math>A</math>",A,SW);
 +
label("<math>B</math>",B,S);
 +
label("<math>C</math>",C,SE);
  
 
[/asy]
 
[/asy]
 
</center>
 
</center>

Revision as of 18:47, 7 March 2018

Problem 4

In $\triangle ABC, AB = AC = 10$ and $BC = 12$. Point $D$ lies strictly between $A$ and $B$ on $\overline{AB}$ and point $E$ lies strictly between $A$ and $C$ on $\overline{AC}$) so that $AD = DE = EC$. Then $AD$ can be expressed in the form $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

Solution 1

[asy] syimport cse5; unitsize(10mm); pathpen=black; dotfactor=3;

pair B = (0,0), A = (6,8), C = (12,0);

label("$A$",A,SW); label("$B$",B,S); label("$C$",C,SE);

[/asy]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2018_AIME_I_Problems/Problem_4&oldid=92893"