Difference between revisions of "2002 AMC 12P Problems/Problem 24"

Revision as of 18:29, 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

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.

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 == 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 ==
 {{AMC12 box|year=2002|ab=P|num-b=23|num-a=25}}
 {{MAA Notice}}

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Difference between revisions of "2002 AMC 12P Problems/Problem 24"

Revision as of 18:29, 10 March 2024

Problem

Solution

See also