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

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- Mar 6th 2010, 04:55 PMdeltaxrayHard question involving trig and circles
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

- Mar 7th 2010, 04:43 AMskeeter
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 .