1979 AHSME Problems/Problem 23
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Problem 23
The edges of a regular tetrahedron with vertices 
, and 
each have length one.
Find the least possible distance between a pair of points 
and 
, where is on edge 
and is on edge 
.
![[asy] size(150); import patterns; pair D=(0,0),C=(1,-1),B=(2.5,-0.2),A=(1,2),AA,BB,CC,DD,P,Q,aux; add("hatch",hatch()); //AA=new A and etc. draw(rotate(100,D)*(A--B--C--D--cycle)); AA=rotate(100,D)*A; BB=rotate(100,D)*D; CC=rotate(100,D)*C; DD=rotate(100,D)*B; aux=midpoint(AA--BB); draw(BB--DD); P=midpoint(AA--aux); aux=midpoint(CC--DD); Q=midpoint(CC--aux); draw(AA--CC,dashed); dot(P); dot(Q); fill(DD--BB--CC--cycle,pattern("hatch")); label("$A$",AA,W); label("$B$",BB,S); label("$C$",CC,E); label("$D$",DD,N); label("$P$",P,S); label("$Q$",Q,E); //Credit to TheMaskedMagician for the diagram[/asy]](http://latex.artofproblemsolving.com/c/2/4/c245e28e642c31b430f5b0086b84ca81883fab4a.png)
Solution
See also
| 1979 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
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