1994 IMO Problems/Problem 2
Let be an isosceles triangle with . is the midpoint of and is the point on the line such that is perpendicular to . is an arbitrary point on different from and . lies on the line and lies on the line such that are distinct and collinear. Prove that is perpendicular to if and only if .
Solution
Let and be on and respectively such that . Then, by the first part of the problem, . Hence, is the midpoint of and , which means that is a parallelogram. Unless and , this is a contradiction since and meet at . Therefore, and , so , as desired.
See Also
1994 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |