1958 AHSME Problems/Problem 48
Problem
Diameter of a circle with center is units. is a point units from , and on . is a point units from , and on . is any point on the circle. Then the broken-line path from to to :
Solution
If is on , then the length is 10, eliminating answer choice .
If is equidistant from and , the length is , eliminating and .
If triangle is right, then angle is right or angle is right. Assume that angle is right. Triangle is right, so . Then, , so the length we are looking for is , eliminating .
Thus, our answer is .
Note: Say you are not convinced that . We can prove this as follows.
Start by simplifying the equation: .
Square both sides: .
Simplify:
Square both sides again: . From here, we can just reverse our steps to get .
See Also
1958 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 47 |
Followed by Problem 49 | |
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