SOLUTION: i the circle, AB is parallel to CD and AB is a diameter. If AB=20 and CD= 2 root 51, how far apart are AB and CD

Question 285080: i the circle, AB is parallel to CD and AB is a diameter. If AB=20 and CD= 2 root 51, how far apart are AB and CD
Answer by toidayma(44) (Show Source): You can put this solution on YOUR website!
Let O the center of the circle. Since AB is the diameter, O is the midpoint of AB.
Let H is the midpoint of CD, we have CH = HD = root(51)
Since OC = OD (= radius), the triangle OCD is an isosceles triangle, therefore OH and CD are perpendicular. Besides, AB//CD -> OH and AB are too perpendicular.
Thus, OH is the distance between AB and CD, you now have to find the length of OH.
Is it much easier now? In the right triangle OHC (angle OHC = 90)we have:
HC = root(51)
OC = radius = AB/2 = 10
Applied Pithagor's, we have: OH^2 = OC^2 - HC^2 = 10^2 - 51 = 49 <-> OH = 7.
So, the distance between AB and CD is 7.
If you find graphing difficult, just tell me.
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