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

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<center>
 
<center>
 
[asy]
 
[asy]
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syimport cse5;
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import cse5;
 
unitsize(10mm);
 
unitsize(10mm);
 
pathpen=black;
 
pathpen=black;

Revision as of 18:48, 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,SW); label("$B$",B,S); label("$C$",C,SE);

[/asy]

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