two chords intersect in a circle. The segments of one chord are 4x and 2y and equal to each other. The segments of the other chord are x+2 and 4y.

Question

two chords intersect in a circle. The segments of one chord are 4x and 2y and equal to each other. The segments of the other chord are x+2 and 4y. Find the legnths of the chords

Answer 1

There's a formula that relates segments of intersecting chords in a circle. If chord AB intersects chord CD at point P, then:

 

(AP)(PB) = (CP)(PD)

 

 

 

For you, this means that:

 

(4x)(2y) = (x+2)(4y)

8xy = 4xy + 8y

4xy = 8y

xy = 2y

x = 2

 

 

 

You're also told that 4x = 2y. So, plug in x = 2 and solve for y:

 

4x = 2y

4(2) = 2y

8 = 2y

4 = y