Difference between revisions of "2009 AIME II Problems/Problem 15"
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| − | Let <math>\overline{MN}</math> be a diameter of a circle with diameter 1. Let A and B be points on one of the semicircular arcs determined by MN such that A is the midpoint of the semicircle and MB=3/ | + | Let <math>\overline{MN}</math> be a diameter of a circle with diameter 1. Let <math>A</math> and <math>B</math> be points on one of the semicircular arcs determined by <math>\overline{MN}</math> such that <math>A</math> is the midpoint of the semicircle and <math>MB= {3}over{5}</math>. Point <math>C</math> lies on the other semicircular arc. Let <math>d</math> be the length of the line segment whose endpoints are the intersections of diameter <math>\overline{MN}</math> with chords <math>\overline{AC}</math> and <math>\overline{BC}</math>. The largest possible value of <math>d</math> can be written in the form r-s*sqrt (t), where r, s, and t are positive integers and t is not divisible by the square of any prime. Find r+s+t. |
Revision as of 04:22, 27 May 2009
Let 
be a diameter of a circle with diameter 1. Let 
and 
be points on one of the semicircular arcs determined by such that is the midpoint of the semicircle and 
. Point 
lies on the other semicircular arc. Let 
be the length of the line segment whose endpoints are the intersections of diameter with chords 
and 
. The largest possible value of can be written in the form r-s*sqrt (t), where r, s, and t are positive integers and t is not divisible by the square of any prime. Find r+s+t.
