1999 AHSME Problems/Problem 19
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
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Solution
Thus and
are integers. By the Pythagorean Theorem,
Thus or
.
See also
1999 AHSME (Problems • Answer Key • Resources) | ||
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 | ||
All AHSME Problems and Solutions |