In Circle O, the midpoint of segment GH is point O. AB = 4x - 2 and CD = 2x + 12.?

Question

In Circle O, the midpoint of segment GH is point O. AB = 4x - 2 and CD = 2x + 12.

Part a) Find the value of x.
Part b) Find the value of AB and CD.
Part c) If GH = 32, find the length of the radius of the circle. Write your answer rounded to the nearest hundredth.
You must show all work for each part to receive full credit.

Picture included: http://img106.imageshack.us/img106/6045/math2ur5.jpg

Answer 1

AB = 4x - 2 and CD = 2x + 12.

Part a) Find the value of x.
AB = CD
=> 4x - 2 = 2x + 12
=> x = 7

Part b) Find the value of AB and CD.
AB = 4(7) - 2= 26
CD = 2(7) + 12= 26

Part c) If GH = 32, find the length of the radius
CO^2 = 16^2 + 13^2

DO THIS YOURSELF to receive full credit

Answer 2

a) Since GO = OH, we have AB = CD (parallel chords equidistant from the center). Therefore, 4x - 2 = 2x + 12, so x = 7.

b) AB = 4(7) - 2 = 26 = 2(7) + 12 = CD.

c) Since O is the midpoint of GH, we know that OH = 16. Also, HD = (1/2)*CD = 13. Now OD is a radius, and in triangle OHD, we have (OH)^2 + (HD)^2 = (OD)^2, so
(16)^2 + (13)^2 = 425 = (OD)^2. Thus, OD = 20.62, correct to the nearest hundredth.