The given semicircle has a diameter of 8 inches (segment ). Chord is half the length and parallel to diameter . Find the distance from the midpoint of chord to the midpoint of diameter .
Source: mathcontest.olemiss.edu 1/21/2008
Let be the midpoint of chord the midpoint of diameter . Since is the midpoint of the diameter, is the center of semicircle.
is an equilateral triangle because ( are radii of the semicircle).
is perpendicular to because is equidistant from the endpoints of .
Apply the Pythagorean theorem to the right :