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BA is tangent to the circle at A and angle DBA = 90 degrees. If AB = 15 and CD = 10, find the radius of the circle.

 

 Dec 8, 2020
 #1
avatar+1162 
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BA is tangent to the circle at A and angle DBA = 90 degrees. If AB = 15 and CD = 10, find the radius of the circle.

 

r = 1/2 [sqrt(102 + 302)]             ( 10 and 30 are the lengths of the legs of an inscribed right-angled triangle )

 Dec 8, 2020
edited by jugoslav  Dec 8, 2020
 #2
avatar+117546 
+2

We can use  the tangent-secant theorem to find   CB

 

We  have  that

 

AB^2  = CB  *( CB + DC)

 

15^2  =  CB ( CB  + 10)

 

225 = CB^2  + 10CB

 

CB^2  + 10CB  -225  =  0

 

Solving this quadratc (taking the positive result) gives us  that CB  =   5sqrt (10)  - 5

 

So  the  radius =  (1/2)DC  + CB   =   (1/2) 10  +  5sqrt (10)  - 5  =

 

5 + 5sqrt (10)   - 5   = 

 

5sqrt (10)

 

 

cool cool cool

 Dec 8, 2020

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