Difference between revisions of "1990 AIME Problems/Problem 14"

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== Problem ==
 
== Problem ==
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The rectangle <math>ABCD^{}_{}</math> below has dimensions <math>AB^{}_{} = 12 \sqrt{3}</math> and <math>BC^{}_{} = 13 \sqrt{3}</math>.  Diagonals <math>\overline{AC}</math> and <math>\overline{BD}</math> intersect at <math>P^{}_{}</math>.  If triangle <math>ABP^{}_{}</math> is cut out and removed, edges <math>\overline{AP}</math> and <math>\overline{BP}</math> are joined, and the figure is then creased along segments <math>\overline{CP}</math> and <math>\overline{DP}</math>, we obtain a triangular pyramid, all four of whose faces are isosceles triangles.  Find the volume of this pyramid.
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[[Image:AIME_1990_Problem_14.png]]
  
 
== Solution ==
 
== Solution ==
 
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== See also ==
 
== See also ==
* [[1990 AIME Problems]]
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{{AIME box|year=1990|num-b=13|num-a=15}}

Revision as of 01:46, 2 March 2007

Problem

The rectangle $ABCD^{}_{}$ below has dimensions $AB^{}_{} = 12 \sqrt{3}$ and $BC^{}_{} = 13 \sqrt{3}$. Diagonals $\overline{AC}$ and $\overline{BD}$ intersect at $P^{}_{}$. If triangle $ABP^{}_{}$ is cut out and removed, edges $\overline{AP}$ and $\overline{BP}$ are joined, and the figure is then creased along segments $\overline{CP}$ and $\overline{DP}$, we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.

AIME 1990 Problem 14.png

Solution

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See also

1990 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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