Difference between revisions of "2002 AMC 12P Problems/Problem 24"
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Assume points <math>P</math>, <math>Q</math>, and <math>R</math> are on faces <math>ABD</math>, <math>ACD</math>, and <math>BCD</math> respectively such that <math>EP \perp ABD</math>, <math>EQ \perp ACD</math>, and <math>ER \perp BCD</math>. | Assume points <math>P</math>, <math>Q</math>, and <math>R</math> are on faces <math>ABD</math>, <math>ACD</math>, and <math>BCD</math> respectively such that <math>EP \perp ABD</math>, <math>EQ \perp ACD</math>, and <math>ER \perp BCD</math>. | ||
| − | Assume points <math>S</math>, <math>T</math>, and <math>U</math> are on | + | Assume points <math>S</math>, <math>T</math>, and <math>U</math> are on edges <math>AB</math>, <math>AC</math>, and <math>BC</math> respectively such that <math>ES \perp AB</math>, <math>ET \perp AC</math>, and <math>EU \perp BC</math>. |
== 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 18:46, 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
Assume points 
, 
, and 
are on faces 
, 
, and 
respectively such that 
, 
, and 
.
Assume points , 
, and 
are on edges 
, 
, and 
respectively such that 
, 
, and 
.
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 | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
