1997 JBMO Problems/Problem 3
Revision as of 18:14, 7 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 3 (credit to stats11) -- inequality chasing)
Problem
Let be a triangle and let be the incenter. Let , be the midpoints of the sides and respectively. The lines and meet at and respectively. Prove that .
Solution
First, by SAS Similarity, so and That means and since is an isosceles triangle. Similarly, making an isosceles as well. Thus, and
By the Triangle Inequality, and , and That means
See Also
1997 JBMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 | ||
All JBMO Problems and Solutions |