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
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 .