SOLUTION: In a circle a chord 30 inches long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is the radius? Answer is 10√ 3... but confused

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Question 1117484: In a circle a chord 30 inches long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is the radius?
Answer is 10√ 3... but confused on how
So I know the radius gets bisected by the chord, does the chord split into 15? How do you find the radius?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The tangent has to be perpendicular to the radius at the point of tangency, and since the chord is parallel to the tangent, the chord is perpendicular to the radius. Therefore the radius bisects the chord, and, in this case it is given that the chord bisects the radius. See http://www.dentonisd.org/cms/lib/TX21000245/Centricity/Domain/926/Circle%20Theorems.pdf

Construct a radius to one endpoint of the chord. This forms a right triangle with sides of 15 and and a hypotenuse of . Use Pythagoras to set up an equation in and solve.

John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
First make a sketch . . . 


You will see a right angled triangle with the legs "one half the radius", "one half of the chord" and the hypotenuse = "radius".


Let x = half of the radius.

Then from Pithagorean theorem you have


 = 

 =   ====>   =  = 75  ====>  x =  = .


The length of the radius = 2x = .

Solved.


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