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Circle O is tangent to AB at A, and angle ABD = 90 degrees. If AB = 12 and CD = \(30\), find the radius of the circle.

 

 Feb 16, 2022
 #1
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Let E be the midpoint of chord  CD

 

Then OE is  perpendicular to  DC

 

And OED  forms a right triangle with DE = 15 , OE  = 12

 

And by the Pythagorean Theorem, OD is a radius =   sqrt  ( DE^2  + OE^2 )  = sqrt ( 15^2 + 12^2 )  =

 

sqrt  [ 225 + 144]   =   sqrt  (369)  ≈ 19.21

 

 

cool cool cool

 Feb 16, 2022

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