2003 IMO Problems/Problem 4
Problem
Let be a cyclic quadrilateral. Let , , and be the feet of perpendiculars from to lines , , and , respectively. Show that if and only if the bisectors of angles and meet on segment .
Solution
Clearly is the Simson Line and , , is cyclic. By angle chasing we have , . Then by we have . Rearranging and using the angle bisector theorem we are done.
See Also
2003 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |