Difference between revisions of "Common internal tangent line"
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*[[Circle]]s with [[center]]s <math>A</math> and <math>B</math> have [[radius |radii]] 3 and 8, respectively. A [[common internal tangent line | common internal tangent]] [[intersect]]s the circles at <math>C</math> and <math>D</math>, respectively. [[Line]]s <math>AB</math> and <math>CD</math> intersect at <math>E</math>, and <math>AE=5</math>. What is <math>CD</math>? <div style="text-align:right;">([[2006 AMC 12A Problems/Problem 16|2006 AMC 12A, #16]])</div> | *[[Circle]]s with [[center]]s <math>A</math> and <math>B</math> have [[radius |radii]] 3 and 8, respectively. A [[common internal tangent line | common internal tangent]] [[intersect]]s the circles at <math>C</math> and <math>D</math>, respectively. [[Line]]s <math>AB</math> and <math>CD</math> intersect at <math>E</math>, and <math>AE=5</math>. What is <math>CD</math>? <div style="text-align:right;">([[2006 AMC 12A Problems/Problem 16|2006 AMC 12A, #16]])</div> | ||
| − | [[Image:2006_AMC12A-16.png|thumb|200px] | + | [[Image:2006_AMC12A-16.png|thumb|200px]] |
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Latest revision as of 11:09, 20 July 2024
A common internal tangent of two circles is a tangent of both circles that intersects the segment joining the centers of two circles.
Problems
Introductory
- Circles with centers
and 
have radii 3 and 8, respectively. A common internal tangent intersects the circles at 
and 
, respectively. Lines 
and 
intersect at 
, and 
. What is ?
and 
have 
and 
, respectively. 
and 
intersect at 
, and 
. What is 
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