1996 IMO Problems/Problem 2
Problem
Let be a point inside triangle such that
Let , be the incenters of triangles , , respectively. Show that , , meet at a point.
Solution
let , be the angle bisectors of and , respectively. Notice that they coincide with line and . Therefore, it suffices to show are concurrent. Let , and . Notice that by angle bisector theorem, we have Therefore, it suffices to show
Now, construct . Connect . We notice that , . Therefore . Therefore, we have
Therefore,
~JoeyW
See Also
1996 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |