1991 AHSME Problems/Problem 10
Problem
Point is units from the center of a circle of radius . How many different chords of the circle contain and have integer lengths?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 29
Solution
Let be the center of the circle, and let the chord passing through that is perpendicular to intersect the circle at and . Then and , so by the Pythagorean Theorem, . By symmetry, .
Therefore, there are chords of integer length passing through .
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
(This problem was also on 2001 State Target Round!)