1965 AHSME Problems/Problem 39
Problem
A foreman noticed an inspector checking a 
"-hole with a 
"-plug and a 
"-plug and suggested that two more gauges
be inserted to be sure that the fit was snug. If the new gauges are alike, then the diameter, 
, of each, to the nearest hundredth of an inch, is:
Solution
![[asy] import geometry; point O = (0,0); point A = (-1/2,0); point B = (1,0); point C, D; // 1", 2", and 3" circles draw(circle(O,3/2)); dot(O); label("O", O, S); draw(circle(A,1)); dot(A); label("A", A, SW); draw(circle(B,1/2)); dot(B); label("B", B, SE); // Other two circles C=(15/14*3/5,15/14*4/5); D=(15/14*3/5,15/14*-4/5); dot(C); label("C",C,N); draw(circle(C, 3/7)); dot(D); label("D",D,S); draw(circle(D, 3/7)); // Segments draw(A--B--C--A); draw(C--O); [/asy]](http://latex.artofproblemsolving.com/1/9/4/1941f460e28056edae5269ebf7ef0529c82ddc5d.png)
See Also
| 1965 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 38 |
Followed by Problem 40 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
