1999 AHSME Problems/Problem 19
From AoPSWiki
Problem
Consider all triangles 
satisfying in the following conditions: 
, 
is a point on 
for which 
, 
and 
are integers, and 
. Among all such triangles, the smallest possible value of is
Solution
Thus 
and are integers. By the Pythagorean Theorem,
Thus 
or 
.
See also
| 1999 AHSME (Problems) | ||
| Preceded by Problem 18 | Followed by Problem 20 | |
| 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 | ||
