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 16: Line 16:
  
 
dot(dotted);
 
dot(dotted);
−
label("$A$",A,SW);
+
label("$A$",A,N);
−
label("$B$",B,S);
+
label("$B$",B,SW);
 
label("$C$",C,SE);
 
label("$C$",C,SE);
  
 
</asy>
 
</asy>
 
</center>
 
</center>

Revision as of 17:49, 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] import cse5; unitsize(10mm); pathpen=black; dotfactor=3; pair B = (0,0), A = (6,8), C = (12,0); D(A--B); D(C--B); D(A--C); dot(dotted); label("$A$",A,N); label("$B$",B,SW); label("$C$",C,SE); [/asy]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2018_AIME_I_Problems/Problem_4&oldid=92897"