Problem:
Three equally spaced parallel lines intersect a circle, creating three chords of lengths , , and . What is the distance between two adjacent parallel lines?
Answer Choices:
A.
B.
C.
D.
E. 7 \dfrac{1}
Solution:
Answer (B): Let the center of the circle be , let its radius be , let chord have length 34 , and let chords and each have length 38 . Because , chords and are equidistant from . Let be the distance from to the midpoint of ; then the distance between adjacent parallel lines is . See the figure. Then the Pythagorean Theorem gives
Thus , so , and the distance between two adjacent parallel lines is . (The circle has radius .)
The problems on this page are the property of the MAA's American Mathematics Competitions