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 <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 17:29, 10 March 2024

Problem

Let $ABCD$ be a regular tetrahedron and Let $E$ be a point inside the face $ABC.$ Denote by $s$ the sum of the distances from $E$ to the faces $DAB, DBC, DCA,$ and by $S$ the sum of the distances from $E$ to the edges $AB, BC, CA.$ Then $\frac{s}{S}$ equals

$\text{(A) }\sqrt{2} \qquad \text{(B) }\frac{2 \sqrt{2}}{3} \qquad \text{(C) }\frac{\sqrt{6}}{2} \qquad \text{(D) }2 \qquad \text{(E) }3$

Solution

See also

2002 AMC 12P (ProblemsAnswer KeyResources)
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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