+556 Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.
+129830 Let d be the distance from the center of the circle to UV
Let the radius of the circle be r
So....by the Pythagorean Theorem
d^2 + (UV /2)^2 = r^2
d^2 + (3)^2 =r^2
d^2 + 9 = r^2 (1)
Let the distance between the center of the circle and YZ = d + 2
By the Pytagorean Theorem
(d +2)^2 + (YZ/2)^2 = r^2
(d + 2)^2 + (4/2)^2 = r^2
(d + 2)^2 + 2^2 = r^2
(d + 2)^2 + 4 = r^2 (2)
Equating (1) and (2)
d^2 + 9 = (d + 2)^2 + 4
d^2 + 9 =d^2 + 4d + 4 +4
1 = 4d
d = (1/4)
And
d^2 + 9 =r^2
(1/4) + 9 = r^2
(37/9) = r^2
To find (1/2) the length of WX
(d + 1)^2 + (WX/2)^2 = r^2
(1/4+ 1)^2 + (WX/2)^2 = 37/9
25/16 + (WX/2)^2 = 37/9
WX^2 / 4 = 37/9 - 25/16
WX^2 / 4 = 367/144
WX^2 = 367/36
WX = sqrt (367) / 6 ≈ 3.19
