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Circle O is tangent to AB at A, and angle ABD = 90 degrees. If AB = 12 and CD = 16, find the radius of the circle.

 

 May 18, 2021
 #1
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Bisect CD  at  M

 

MD  =   8

 

Draw   OM  =  BA   =   12

 

We  have  right triangle  DOM   where  OD  =  the  radius of the circle   and  hypotenuse of DOM

 

Using  the  Pythagorean Theorem

 

OD   =sqrt  ( OM^2  + MD^2 )  =  sqrt  ( 12^2  +  8^2)  =  sqrt ( 144  + 64)  = sqrt  (208)   = 4sqrt (13)  = the  radius

 

cool cool cool

 May 18, 2021
 #2
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I wish I was as smart as you 🙁

Guest May 18, 2021
 #3
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r = 1/2{sqrt[CD2 + (2 * AB)2]}

 May 19, 2021

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