1995 IMO Problems/Problem 5
Problem
Let be a convex hexagon with and , such that . Suppose and are points in the interior of the hexagon such that . Prove that .
Solution
Draw and to make equilateral and , and draw points and such that , , directed angle , and directed angle to make equilateral and . Notice that is on the circumcircle of and is on the circumcircle of . By Ptolemy, and . So, Notice that octagon is symmetric about . So, . --tigerzhang
See Also
1995 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |