Difference between revisions of "1994 AIME Problems/Problem 2"
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== Problem == | == Problem == | ||
| + | A circle with diameter <math>\overline{PQ}\,</math> of length 10 is internally tangent at <math>P^{}_{}</math> to a circle of radius 20. Square <math>ABCD\,</math> is constructed with <math>A\,</math> and <math>B\,</math> on the larger circle, <math>\overline{CD}\,</math> tangent at <math>Q\,</math> to the smaller circle, and the smaller circle outside <math>ABCD\,</math>. The length of <math>\overline{AB}\,</math> can be written in the form <math>m + \sqrt{n}\,</math>, where <math>m\,</math> and <math>n\,</math> are integers. Find <math>m + n\,</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1994|num-b=1|num-a=3}} | |
Revision as of 23:21, 28 March 2007
Problem
A circle with diameter 
of length 10 is internally tangent at 
to a circle of radius 20. Square 
is constructed with 
and 
on the larger circle, 
tangent at 
to the smaller circle, and the smaller circle outside . The length of 
can be written in the form 
, where 
and 
are integers. Find 
.
Solution
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See also
| 1994 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
