Homework Help

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

user profile pic

novjb | Salutatorian

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

dislike 0 like

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

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

1 Answer | Add Yours

user profile pic

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

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

dislike 1 like

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`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes