The length of a chord is equal to its distance to the center of the circle. a second chord in the same circle is twice as long as the first one. how far is the second chord from the center?

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.

Step-by-step explanation:

The length of the chord AB is the same as the distance OC from the center to the cord. Let OC=2x, then CA=x. By the Pythagorean theorem, the radius r of the circle is

The length of the arc ED is 4x.

Consider right triangle EFO. In this triangle, EF=2x, EO=r, then the distance OF is

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.