sketch in the radii to the chord endpoints.

let the endpoints be A and B, circle center O, and intersection of radius w/ chord be point C.

is the acute angle between the chord and intersecting radius.

using the cosine law ...

now consider , which is supplementary to .

using the cosine law again ...

set the two expressions for equal and solve for either x in terms of r or r in terms of x, then determine the value of .