SOLUTION: A line segment joining two points on the circumferences of a circle is one inch from the center of the circle at its closest point. If the circle has two inch radius. What is the l
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Question 437387: A line segment joining two points on the circumferences of a circle is one inch from the center of the circle at its closest point. If the circle has two inch radius. What is the length of the line??
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Construct the 1 inch perpendicular from the chord to the center. This segment, that portion of the chord from the intersection of the perpendicular to either endpoint of the chord, and the radius to either endpoint of the chord form a right triangle for which the short leg measures 1/2 of the hypotenuse (the radius). Therefore this is a 30-60-90 degreee right triangle and the measure of the long leg is the measure of the hypotenuse times the square root of three divided by two.
In this case the long leg is 
Any perpendicular to a chord that passes through the center of a circle bisects the chord. Hence the chord measures twice the long leg of the triangle:
inches.
Use your calculator if you need a numeric approximation of the answer, but round to the nearest whole inch since the given measurements are given to whole number precision.
John
My calculator said it, I believe it, that settles it
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