SOLUTION: Please Help!!! I'm unsure how to work this problem out. I'm given the answer Radius=5.67cm but I am having trouble working the problem out to get this answer. A piece of a broke

Question 938859: Please Help!!! I'm unsure how to work this problem out. I'm given the answer Radius=5.67cm but I am having trouble working the problem out to get this answer.
A piece of a broken wheel is shown. It was taken to a machine shop to be replaced with a new �whole� wheel. Find the radius of the wheel if AC = 10 cm, BD = 3cm, and D is the midpoint AC of. Round to the nearest hundredth.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please Help!!! I'm unsure how to work this problem out. I'm given the answer Radius=5.67cm but I am having trouble working the problem out to get this answer.
A piece of a broken wheel is shown. It was taken to a machine shop to be replaced with a new �whole� wheel. Find the radius of the wheel if AC = 10 cm, BD = 3cm, and D is the midpoint AC of. Round to the nearest hundredth.
***
let r=radius
construct a line extending BD to the center
Connect the ends of AC to the center
You now have a right triangle with legs of (r-3) and 5 and hypotenuse=r
5^2+(r-3)^2=r^2
25+r^2-6r+9=r^2
6r=34
r=5.67 cm
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