University of South Carolina High School Math Contest/1993 Exam/Problem 28
Suppose is a triangle with 3 acute angles and . Then the point
(A) can be in the 1st quadrant and can be in the 2nd quadrant only
(B) can be in the 3rd quadrant and can be in the 4th quadrant only
(C) can be in the 2nd quadrant and can be in the 3rd quadrant only
(D) can be in the 2nd quadrant only
(E) can be in any of the 4 quadrants
First note that and . From these, we deduce that the value and the value of the coordinates will always be positive and thus the point can only be in the first quadrant.