+0  
 
-1
68
2
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A circle passes through the point (12,0), and is tangent to the y-axis at the point (0,3), as shown. Find the radius of the circle.

 Jul 28, 2020
 #1
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+1

he circle is tangent to the y-axis at  (0, 2) , so the y-coordinate of the center must be  2  .

 

We know..

 

(x - h)2 + (y - 2)2  =  r2      , where  h  is the x-coordinate of the vertex and  r  is the radius.

 

(0 - h)2 + (2 - 2)2  =  r2     →​     h2  =  r2     →     h  =  ± r

 

(8 - h)2 + (0 - 2)2  =  r2     →​     (8 - h)2 + 4  =  r2

 

In the last equation, substitute  ± r  in for  h .

 

(8 - ± r)2 + 4  =  r2

 

(8 + r)2 + 4  =  r2          or          (8 - r)2 + 4  =  r2

64 + 16r + r2 + 4  =  r2 64 - 16r + r2 + 4  =  r2

68 + 16r  =  0 68 - 16r  =  0

r  =  -68/16 r  =  68/16

r  =  -4.25 r  =  4.25

 

Since  r  is a distance,  r  =  4.25

 Jul 28, 2020
 #2
avatar+1326 
+1

Hello, Guest!

 

If radius   r = 4.25 then the diameter is 8.5?!? cheeky It's not possible!!!! The diameter is over 12 units.

 

Angle (ACO) = arctan(3 / 12) = 14.03624347º

 

AD = [sqrt(32 + 122)] / 2 = 6.184658438

 

AB = (AD) / cos(ACO) = 6.375

 

The radius of a circle is 6.375 units  wink

 

Dragan  Jul 28, 2020

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