SOLUTION: Chord PQ is perpendicular bisector of radius OA of a circle with center O (A is a point on the edge of the circle). If the length of the arc PAQ = 2pie/3. What is the length of the

Question 1085256: Chord PQ is perpendicular bisector of radius OA of a circle with center O (A is a point on the edge of the circle). If the length of the arc PAQ = 2pie/3. What is the length of the chord PQ?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Here is a sketch, with the midpoint of OA labeled as R:
Take a good look at right triangle OQR.
The lengths are the radius, , of the circle.
is half of that radius.
That tells you that the short leg of right triangle OQR is half the hypotenuse.
It means that
(from applying the Pythagorean theorem).
It also means (considering trigonometric ratios for the angles of OQR) that
OQR is a 30-60-90 triangle, with a angle at O,
which makes angle and arc measure ,
or of the whole circle.
If is the length of arc ,
then is , the length of the circumference.
Then, , , and .
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