Difference between revisions of "Mock AIME 1 2007-2008 Problems/Problem 11"
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== Solution == | == Solution == | ||
− | + | <center><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></center> | ||
{{solution}} | {{solution}} | ||
Revision as of 16:39, 24 April 2008
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
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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 |