A radius of a circle divides a chord in the ratio 2:1 and is bisected by the chord. Show that the cosine of the angle between the radius and the chord is
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 .