What is the length of the cord with a radius of 10 feet and the height of the segment is 2 feet?

Let the chord be AB and the centre of the circle be C.

Draw a radius to points A and B. Draw a line perpendicular to and bisecting the chord at D - this will be another radius which bisects the angle formed by the other two radii.

As the height of the segment is 2' then the length CD = 10 - 2 = 8'

∆CAD (& ∆CBD) are right angled triangles with CA, the hypotenuse = 10' and CD = 8'

Therefore AD² + 8² = 10² : AD² = 100 - 64 = 36 : AD = √ 36 = 6

AD is half AB and therefore the length of the chord is 2 x 6 = 12'