Difference between revisions of "1990 AHSME Problems/Problem 6"
(Created page with "== Problem == Points <math>A</math> and <math>B</math> are <math>5</math> units apart. How many lines in a given plane containing <math>A</math> and <math>B</math> are <math>2</...") |
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== Solution == | == Solution == | ||
| − | <math>\fbox{D}</math> | + | The lines have to be tangent to both of these circles. |
| + | <asy> | ||
| + | dot((0,0));dot((5,0)); | ||
| + | label("$A$",(0,0),S);label("$B$",(5,0),S); | ||
| + | draw(Circle((0,0),2));draw(Circle((5,0),3)); | ||
| + | real m = sqrt(6)/12; | ||
| + | path p = (-.4-3,4*sqrt(6)/5-3*m)--(4.4+4,6*sqrt(6)/5+4*m); | ||
| + | draw(p,dotted);draw(reflect((0,0),(1,0))*p,dotted);draw((2,-4)--(2,4),dotted); | ||
| + | </asy> | ||
| + | By inspection, <math>\fbox{D}</math> | ||
== See also == | == See also == | ||
Latest revision as of 03:39, 4 February 2016
Problem
Points 
and 
are 
units apart. How many lines in a given plane containing and are 
units from and 
units from ?
Solution
The lines have to be tangent to both of these circles.
![[asy] dot((0,0));dot((5,0)); label("$A$",(0,0),S);label("$B$",(5,0),S); draw(Circle((0,0),2));draw(Circle((5,0),3)); real m = sqrt(6)/12; path p = (-.4-3,4*sqrt(6)/5-3*m)--(4.4+4,6*sqrt(6)/5+4*m); draw(p,dotted);draw(reflect((0,0),(1,0))*p,dotted);draw((2,-4)--(2,4),dotted); [/asy]](http://latex.artofproblemsolving.com/1/3/5/1359b819a7fb7774e0addfffc6a6c0a3a8f40e2d.png)
By inspection, 
See also
| 1990 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
