SOLUTION: PQ is a diameter of a circle centered at O. R is a point on the circle such that angle ROQ is 120°. If the circumference of the circle is 9π, then what is the length of chord

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Question 1131646: PQ is a diameter of a circle centered at O. R is a point on the circle such that angle ROQ is 120°. If the circumference of the circle is 9π, then what is the length of chord PR?
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


The circumference of the circle is given as 9pi; the radius of the circle is the circumference divided by 2pi. So the radius of the circle is 9/2, or 4.5.

If angle ROQ is 120 degrees, then angle ROP is 60 degrees. Then, since RO and PO are both radii of the circle, triangle ROP is equilateral.

And that means chord PR is the same length as the radius of the circle.

ANSWER: The length of chord PR is 4.5.