Difference between revisions of "2021 AIME I Problems/Problem 13"
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==Problem== | ==Problem== | ||
| − | + | Circles <math>\omega_1</math> and <math>\omega_2</math> with radii <math>961</math> and <math>625</math>, respectively, intersect at distinct points <math>A</math> and <math>B</math>. A third circle <math>\omega</math> is externally tangent to both <math>\omega_1</math> and <math>\omega_2</math>. Suppose line <math>AB</math> intersects <math>\omega</math> at two points <math>P</math> and <math>Q</math> such that the measure of minor arc <math>\widehat{PQ}</math> is <math>120^{\circ}</math>. What is the distance between the centers of <math>\omega_1</math> and <math>\omega_2</math>? | |
==Solution== | ==Solution== | ||
| + | <math>672</math> | ||
| + | |||
==See also== | ==See also== | ||
{{AIME box|year=2021|n=I|num-b=12|num-a=14}} | {{AIME box|year=2021|n=I|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:47, 11 March 2021
Problem
Circles 
and 
with radii 
and 
, respectively, intersect at distinct points 
and 
. A third circle 
is externally tangent to both and . Suppose line 
intersects at two points 
and 
such that the measure of minor arc 
is 
. What is the distance between the centers of and ?
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
