Difference between revisions of "1995 AIME Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | In a circle of radius 42, two chords of length 78 intersect at a point whose distance from the center is 18. The two chords divide the interior of the circle into four regions. Two of these regions are bordered by segments of unequal lenghts, and the area of either of them can be expressed uniquley in the form <math>\displaystyle m\pi-n\sqrt{d},</math> where <math>\displaystyle m, n,</math> and <math>\displaystyle d_{}</math> are positive integers and <math>\displaystyle d_{}</math> is not divisible by the square of any prime number. Find <math>\displaystyle m+n+d.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_13|Previous Problem]] | ||
| + | * [[1995_AIME_Problems/Problem_15|Next Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 00:32, 22 January 2007
Problem
In a circle of radius 42, two chords of length 78 intersect at a point whose distance from the center is 18. The two chords divide the interior of the circle into four regions. Two of these regions are bordered by segments of unequal lenghts, and the area of either of them can be expressed uniquley in the form 
where 
and 
are positive integers and is not divisible by the square of any prime number. Find 
