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

(→‎Solution 1)
(→‎Solution 1)
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==Solution 1==
 
==Solution 1==
 
<center>
 
<center>
−
[asy]
+
<asy>
 
import cse5;
 
import cse5;
 
unitsize(10mm);
 
unitsize(10mm);
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dot(dotted);
 
dot(dotted);
−
label("<math>A</math>",A,SW);
+
label("$A$",A,SW);
−
label("<math>B</math>",B,S);
+
label("$B$",B,S);
−
label("<math>C</math>",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,SW); label("$B$",B,S); label("$C$",C,SE); [/asy]

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