Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 25"
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Let the circle we are looking for be <math>(x-h)^{2}+(y-k)^{2}=r^{2}</math> where <math>(h,k)</math> is obviously the center. Plugging in points <math>(6,0)</math> and <math>(0,2)</math> gives us that <math>3k-h=8</math>. Seeing our answer choices, none of the points work, thus our answer is E. | Let the circle we are looking for be <math>(x-h)^{2}+(y-k)^{2}=r^{2}</math> where <math>(h,k)</math> is obviously the center. Plugging in points <math>(6,0)</math> and <math>(0,2)</math> gives us that <math>3k-h=8</math>. Seeing our answer choices, none of the points work, thus our answer is E. | ||
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− | * [[University of South Carolina High School Math Contest/1993 Exam]] | + | |
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 24|Previous Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 26|Next Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam|Back to Exam]] | ||
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+ | [[Category:Intermediate Algebra Problems]] | ||
+ | [[Category:Intermediate Geometry Problems]] |
Revision as of 10:47, 23 July 2006
Problem
What is the center of the circle passing through the point and tangent to the circle
at
? (Two circles are tangent at a point
if they intersect at
and at no other point.)
![$\mathrm{(A) \ }(0,-6) \qquad \mathrm{(B) \ } (1,-9) \qquad \mathrm{(C) \ } (-1,-9) \qquad \mathrm{(D) \ } (0,-9) \qquad \mathrm{(E) \ } \rm{none \ } \rm{of \ } \rm{these}$](http://latex.artofproblemsolving.com/0/0/b/00bc059af7b25de3ab7957a6c887569ef06b1fdd.png)
Solution
Let the circle we are looking for be where
is obviously the center. Plugging in points
and
gives us that
. Seeing our answer choices, none of the points work, thus our answer is E.