Difference between revisions of "2017 AMC 10A Problems/Problem 17"
(→Problem) |
|||
| Line 3: | Line 3: | ||
<math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 5\qquad\mathrm{(C)}\ 3\sqrt{5}\qquad\mathrm{(D)}\ 7\qquad\mathrm{(E)}\ 5\sqrt{2}</math> | <math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 5\qquad\mathrm{(C)}\ 3\sqrt{5}\qquad\mathrm{(D)}\ 7\qquad\mathrm{(E)}\ 5\sqrt{2}</math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | Because <math>P</math>, <math>Q</math>, <math>R</math>, and <math>S</math> are integers there are only a few coordinates that actually satisfy the equation. The coordinates are <math>(\pm 3,\pm 4), (\pm 4, \pm 3), (0,\pm 5),</math> and <math>(\pm 5,0).</math> | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=A|num-b=16|num-a=18}} | {{AMC10 box|year=2017|ab=A|num-b=16|num-a=18}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:14, 8 February 2017
Problem
Distinct points 
, 
, 
, 
lie on the circle 
and have integer coordinates. The distances 
and 
are irrational numbers. What is the greatest possible value of the ratio 
?
Solution
Because , , , and are integers there are only a few coordinates that actually satisfy the equation. The coordinates are 
and 
See Also
| 2017 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
