the radius of a curvature is 10ft and the height of the segment is 2ft. What is the length of the chord

1 answer

Let the length of the chord be x.
Draw a perpendicular bisector to the chord and let it intersect the circles at A and B. The mid-point of the chord is M.

Since the radius is 10 ft, the diameter is 20 ft. mAM=2 ft, and mMB = 20-2=18 ft.
By the property of intersecting chords,
(x/2)² = mAM . mMB
=2*18
=36
x/2=6 ft
x= 12 ft.