Difference between revisions of "2002 AMC 12P Problems/Problem 24"
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== Solution == | == Solution == | ||
| − | We create a coordinate system for the point <math>E = (x, y)</math>. Let <math>x</math> be the distance from | + | We create a coordinate system for the point <math>E = (x, y)</math>. Let <math>x</math> be the distance from <math>AB</math>, and let <math>y</math> be the distance <math>EF</math>, where <math>F </math> is on <math>AC</math> and <math>EF</math> is parallel to <math>AB</math>. Call the distances from <math>E</math> to <math>ABD</math>, <math>ACD</math>, and <math>BCD</math> <math>d_a</math>, <math>d_b</math>, and <math>d_c</math>, respectively. |
== See also == | == See also == | ||
{{AMC12 box|year=2002|ab=P|num-b=23|num-a=25}} | {{AMC12 box|year=2002|ab=P|num-b=23|num-a=25}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:25, 10 March 2024
Problem
Let 
be a regular tetrahedron and Let 
be a point inside the face 
Denote by 
the sum of the distances from to the faces 
and by 
the sum of the distances from to the edges 
Then 
equals
Solution
We create a coordinate system for the point 
. Let 
be the distance from 
, and let 
be the distance 
, where 
is on 
and is parallel to . Call the distances from to 
, 
, and 
, 
, and 
, respectively.
See also
| 2002 AMC 12P (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
