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(52898) (Show Source):
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A circle passes through A and B and is tangent to CD. Its circumference, in cm, is
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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
