Difference between revisions of "2002 IMO Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | <math>BC</math> is a diameter of a circle center <math>O</math>. <math>A</math> is any point on the circle with <math>\angle AOC \not\le 60^\circ</math>. | + | <math>BC</math> is a diameter of a circle center <math>O</math>. <math>A</math> is any point on the circle with <math>\angle AOC \not\le 60^\circ</math>. <math>EF</math> is the chord which is the perpendicular bisector of <math>AO</math>. <math>D</math> is the midpoint of the minor arc <math>AB</math>. The line through <math>O</math> parallel to <math>AD</math> meets <math>AC</math> at <math>J</math>. Show that <math>J</math> is the incenter of triangle <math>CEF</math>. |
| − | <math>EF</math> is the chord which is the perpendicular bisector of <math>AO</math>. <math>D</math> is the midpoint of the minor arc <math>AB</math>. The line through | ||
| − | <math>O</math> parallel to <math>AD</math> meets <math>AC</math> at <math>J</math>. Show that <math>J</math> is the incenter of triangle <math>CEF</math>. | ||
==Solution== | ==Solution== | ||
Latest revision as of 08:32, 5 July 2024
Problem
is a diameter of a circle center 
. 
is any point on the circle with 
. 
is the chord which is the perpendicular bisector of 
. 
is the midpoint of the minor arc 
. The line through parallel to 
meets 
at 
. Show that is the incenter of triangle 
.
Solution
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See Also
| 2002 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
