I think this will be the last one.
Find the radius of circle C if the measure of anglePQR=24° and the length of arc PR is 8pi.
Answers:
a.15 b.20 c.30 d.60 e.45
The diagram looks like a circle with its center at C. At a point on the edge of the circle is Q with lines reaching out to P and R at 24°. The arc between them is 8pi. Hope that helps
24 degrees = 24 * pi/180 = pi*(2/15) radians
(arc length)/radius = pi*(2/15)
radius = (8 pi)/[(2/15)*pi]
= 60
To find the radius of circle C, we'll need to use the relationship between angles and arcs.
The formula to find the length of an arc in a circle is given by:
Arc length = (angle/360) * (2 * pi * radius)
In this case, we know that the measure of angle PQR is 24° and the length of arc PR is 8pi.
Let's substitute the values into the formula:
8pi = (24/360) * (2 * pi * radius)
Simplifying the equation:
8pi = (1/15) * (2 * pi * radius)
Multiplying both sides of the equation by 15:
120pi = 2pi * radius
Canceling out pi on both sides:
120 = 2 * radius
Dividing both sides by 2:
60 = radius
Therefore, the radius of circle C is 60.
The correct answer is option d. 60.