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.)
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.