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# If circle C has a diameter of 13, solve for x.

novjb | Salutatorian

Posted September 8, 2013 at 9:51 PM via web

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If circle C has a diameter of 13, solve for x.

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted September 8, 2013 at 10:23 PM (Answer #1)

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Since Chord `bar(DE)`` ` is perpendicular to the Diameter AB, it creates a right triangle DCF, and the hypotenuse is a radius, so it is exactly one half the length of the 13 diameter, or 6.5.

The diagram shows that `bar(DF)` is exactly 6 units, so the cosine of `/_D` is `6/6.5` We find `arccos 6/6.5~~22.62 deg` Then ``we multiply the sine of `/_D` by 6.5, to find the distance from F to the Center, subtract that from the Radius, and the remainder will be x.

`6.5 xx sin 2.62=2.5` using the calculator to maintain exact numbers.  `6.5-2.5=x=4`

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