MathDB

The points

A

and

B

lie on a horizontal line over a vertical plane. We consider the semicircumference passing through

A

and

B

that lies under the horizontal line. A segment of length

a

, with the same diameter that the semicircumference, moves in a way that always contains the point

A

and one of its extremes lies always on the semicircumference. Determine the value of the cosine of the angle between this segment and the horizontal line that makes the medium point of the segment to be as down as possible.

Problem Statement