Difference between revisions of "2017 AMC 12B Problems/Problem 6"
Silverlion (talk | contribs) (→Solution) |
(→Problem 6) |
||
| Line 1: | Line 1: | ||
==Problem 6== | ==Problem 6== | ||
The circle having <math>(0,0)</math> and <math>(8,6)</math> as the endpoints of a diameter intersects the <math>x</math>-axis at a second point. What is the <math>x</math>-coordinate of this point? | The circle having <math>(0,0)</math> and <math>(8,6)</math> as the endpoints of a diameter intersects the <math>x</math>-axis at a second point. What is the <math>x</math>-coordinate of this point? | ||
| + | |||
| + | <math> \textbf{(A) } 4\sqrt{2} \qquad\textbf{(B) } 6 \qquad\textbf{(C) } 5\sqrt{2} \qquad\textbf{(D) } 8 \qquad\textbf{(E) } 6\sqrt{2} </math> | ||
==Solution== | ==Solution== | ||
Revision as of 00:51, 10 September 2017
Problem 6
The circle having 
and 
as the endpoints of a diameter intersects the 
-axis at a second point. What is the -coordinate of this point?
Solution
Because the two points are on a diameter, the center must be halfway between them at the point (4,3). The distance from (0,0) to (4,3) is 5 so the circle has radius 5. Thus, the equation of the circle is 
.
To find the x-intercept, y must be 0, so 
, so 
, 
, 
.
Written by: SilverLion
See Also
| 2017 AMC 12B (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 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
