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Help.

NotSoSmart  Apr 12, 2017
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 #1
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+2

This one is a little difficult....

 

Assuming that CD is a tangent, ODC forms a right triangle with OC the hypotenuse  and CD  a leg

 

So....the other leg (OD)  can be found with the Pythagorean Theorem.....note that OD  = OB =the radius of the circle, r

 

OD  =   sqrt ( OC^2  - CD^2)      and we can write

 

r  =  sqrt ( [CB + OB]^2  - CD^2  )

 

r = sqrt  ( [ 14 + r ]^2  -  25^2 )        square both sides

 

r^2  =  [14 + r ]^2  -  625

 

r^2   =  196 + 28r  + r^2   -  625     subtract r^2 from both sides

 

0 = -429  + 28r       add 429 to both sides

 

429  =  28r       divide both sides by 28

 

15.3  = r

 

And the diameter is twice this  =  30.6

 

 

cool cool cool

CPhill  Apr 12, 2017

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