1988 AHSME Problems/Problem 27
Problem
In the figure, , and is tangent to the circle with center and diameter . In which one of the following cases is the area of an integer?
Solution
Let and be the intersections of lines and with the circle. One can prove that is a rectangle, so .
In order for the area of trapezoid to be an integer, the expression must be an integer, so must be rational.
By Power of a Point, , so must be a perfect square. Among the choices, the only one where is a perfect square is
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.