Art of Problem Solving

2018 AIME I Problems/Problem 4: Difference between revisions

Boobootm (talk | contribs)
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==Solution 1==
==Solution 1==
<center><asy>import cse5;
<center>
[asy]
syimport cse5;
unitsize(10mm);
unitsize(10mm);
pathpen=black;
pathpen=black;
Line 10: Line 12:
pair B = (0,0), pair A = (6,8), pair C = (12,0)
pair B = (0,0), pair A = (6,8), pair C = (12,0)


</asy></center>
[/asy]
</center>

Revision as of 17:44, 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), pair A = (6,8), pair C = (12,0)

[/asy]