Difference between revisions of "Mock AIME 6 2006-2007 Problems/Problem 13"
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==Problem== | ==Problem== | ||
| − | Consider two circles of different sizes that do not intersect. The smaller circle has center <math>O</math>. Label the intersection of their common external tangents <math>P</math>. A common internal tangent | + | Consider two circles of different sizes that do not intersect. The smaller circle has center <math>O</math>. Label the intersection of their common external tangents <math>P</math>. A common internal tangent intersects the common external tangents at points <math>A</math> and <math>B</math>. Given that the radius of the larger circle is <math>11</math>, <math>PO=3</math>, and <math>AB=20\sqrt{2}</math>, what is the square of the area of triangle <math>PBA</math>? |
==Solution== | ==Solution== | ||
[[File:Mock_AIME_6_P13.png|600px]] | [[File:Mock_AIME_6_P13.png|600px]] | ||
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~Tomas Diaz. orders@tomasdiaz.com | ~Tomas Diaz. orders@tomasdiaz.com | ||
{{alternate solutions}} | {{alternate solutions}} | ||
Revision as of 03:13, 26 November 2023
Problem
Consider two circles of different sizes that do not intersect. The smaller circle has center 
. Label the intersection of their common external tangents 
. A common internal tangent intersects the common external tangents at points 
and 
. Given that the radius of the larger circle is 
, 
, and 
, what is the square of the area of triangle 
?
Solution
~Tomas Diaz. orders@tomasdiaz.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
