University of South Carolina High School Math Contest/1993 Exam/Problem 28
Problem
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
Solution
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First note that and
.
Since ,
and
have the same sign. Similarly,
and
have the same sign.
Notice that . Then
can only lie in the 2nd and 4th quadrants.