SOLUTION: A circle passes through A and B and is tangent to CD. Its circumference, in cm, is? https://ibb.co/ncxbQ6Y

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Question 1199928: A circle passes through A and B and is tangent to CD. Its circumference, in cm, is?
https://ibb.co/ncxbQ6Y
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
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A circle passes through A and B and is tangent to CD. Its circumference, in cm, is
~~~~~~~~~~~~~~~~~~ 

Draw the circle as described.


Let point O be the center of the circle.  Let R be the radius of the circle.

Let point E be midpoint of the segment AB.


Consider right angled triangle OED.


    Its leg OE is R-3 cm long.

    Its leg ED is 2 cm long.

    Its hypotenuse OD is the radius R of the circle.


Now apply Pythagoream theorem

    R^2 = (R-3)^2 + 2^2.

Simplify and find R

    R^2 = R^2 - 6R + 9 + 4

    6R = 13

     R = .


Hence, the circumference of the circle is 

     =  =  =  =  = 13.57 cm  (rounded).  ANSWER

Solved.



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