2009 IMO Problems/Problem 2
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[hide]Problem
Let be a triangle with circumcentre . The points and are interior points of the sides and respectively. Let and be the midpoints of the segments and , respectively, and let be the circle passing through and . Suppose that the line is tangent to the circle . Prove that .
Author: Sergei Berlov, Russia
Video Solution
Solution
Diagram
Diagram by qwertysri987
By parallel lines and the tangency condition, Similarly, so AA similarity implies Let denote the circumcircle of and its circumradius. As both and are inside
It follows that
See Also
2009 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |