Difference between revisions of "1983 IMO Problems/Problem 2"
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Let <math>A</math> be one of the two distinct points of intersection of two unequal coplanar circles <math>C1</math> and <math>C2</math> with centers <math>O1</math> and <math>O2</math>, respectively. One of the common tangents to the circles touches <math>C1</math> at <math>P1</math> and <math>C2</math> at <math>P2</math>, while the other touches <math>C1</math> at <math>Q1</math> and <math>C2</math> at <math>Q2</math>. Let <math>M1</math> be the midpoint of <math>P1</math>. | Let <math>A</math> be one of the two distinct points of intersection of two unequal coplanar circles <math>C1</math> and <math>C2</math> with centers <math>O1</math> and <math>O2</math>, respectively. One of the common tangents to the circles touches <math>C1</math> at <math>P1</math> and <math>C2</math> at <math>P2</math>, while the other touches <math>C1</math> at <math>Q1</math> and <math>C2</math> at <math>Q2</math>. Let <math>M1</math> be the midpoint of <math>P1</math>. | ||
{{IMO box|year=1983|num-b=1|num-a=3}} | {{IMO box|year=1983|num-b=1|num-a=3}} | ||
Revision as of 21:36, 31 January 2016
Problem
Let 
be one of the two distinct points of intersection of two unequal coplanar circles 
and 
with centers 
and 
, respectively. One of the common tangents to the circles touches at 
and at 
, while the other touches at 
and at 
. Let 
be the midpoint of .
| 1983 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
