Mock AIME 1 2007-2008 Problems/Problem 11
Problem
is inscribed inside
such that
lie on
, respectively. The circumcircles of
have centers
, respectively. Also,
, and
. The length of
can be written in the form
, where
and
are relatively prime integers. Find
.
Solution
![[asy] pointpen = black; pathpen = black; pair A=(0,0),B=(23,0),C=IP(Circle(A,24),Circle(B,25)); D(MP("A",A)--MP("B",B)--MP("C",C,N)--cycle); pair D=(B+C)/2,E=(A+C)/2,F=(A+B)/2; D(circumcircle(MP("D",D),MP("E",E),C)); D(circumcircle(B,MP("F",F),D)); D(circumcircle(A,F,E)); [/asy]](http://latex.artofproblemsolving.com/8/1/d/81da80714c8c10e338bd083834a7a242b4d9178f.png)
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See also
Mock AIME 1 2007-2008 (Problems, Source) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |