Difference between revisions of "2009 AIME II Problems/Problem 15"
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| − | Let \overline{MN} 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=3/5. Point C lies on the other semicircular arc. Let d be the length of the line segment whose endpoints are the intersections of diameter MN with chords AC and BC. The largest possible value of d 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. | + | 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=3/5. Point C lies on the other semicircular arc. Let d be the length of the line segment whose endpoints are the intersections of diameter MN with chords AC and BC. The largest possible value of d 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 04:19, 27 May 2009
Let 
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=3/5. Point C lies on the other semicircular arc. Let d be the length of the line segment whose endpoints are the intersections of diameter MN with chords AC and BC. The largest possible value of d 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.
