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 18:25, 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 |
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