1960 AHSME Problems/Problem 35
Problem 35
From point outside a circle, with a circumference of units, a tangent is drawn. Also from a secant is drawn dividing the circle into unequal arcs with lengths and . It is found that , the length of the tangent, is the mean proportional between and . If and are integers, then may have the following number of values:
Solution
By definition of mean proportional, . Since , .
With trial and error, note that when , and when , . These values work since another tangent line can be drawn from , and the angle between the tangent and secant can decrease to match the values of and . Thus, the answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 34 |
Followed by Problem 36 | |
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