Difference between revisions of "2017 UNCO Math Contest II Problems/Problem 1"
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== Problem == | == Problem == | ||
| + | <asy> | ||
| + | pair A=24*dir(40),B=15*dir(220); | ||
| + | |||
| + | pair C1=(0,0),C2=(52,0); | ||
| + | draw(circle(C1,24),black); | ||
| + | draw(circle(C2,15),black); | ||
| + | |||
| + | draw(C1--C2,dot); | ||
| + | draw(A--(B+C2)); | ||
| + | </asy> | ||
| + | |||
| + | A circle has radius 24, a second circle has radius 15, and the centers of the two circles are 52 | ||
| + | units apart. A line tangent to both circles crosses the line connecting the two centers at a point | ||
| + | P between the two centers. How much farther is P from the center of the bigger circle than it | ||
| + | is from the center of the smaller circle? | ||
== Solution == | == Solution == | ||
Revision as of 00:12, 20 May 2017
Problem
![[asy] pair A=24*dir(40),B=15*dir(220); pair C1=(0,0),C2=(52,0); draw(circle(C1,24),black); draw(circle(C2,15),black); draw(C1--C2,dot); draw(A--(B+C2)); [/asy]](http://latex.artofproblemsolving.com/c/1/9/c195a306330c977fedd7ae437b3d16be5e2a8227.png)
A circle has radius 24, a second circle has radius 15, and the centers of the two circles are 52 units apart. A line tangent to both circles crosses the line connecting the two centers at a point P between the two centers. How much farther is P from the center of the bigger circle than it is from the center of the smaller circle?
Solution
See also
| 2017 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
