Difference between revisions of "1965 AHSME Problems/Problem 39"
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== Solution == | == 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> | ||
| + | |||
<math>\fbox{B}</math> | <math>\fbox{B}</math> | ||
Revision as of 12:33, 20 July 2024
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 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
