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a. What is the area and circumference of circle ? Explain how you calculated this answer.
b. If the arc measure of arc is and the arc measure of arc is , what is the angle measure of angle ? Explain how you calculated this answer.
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Can you find the length of DR?
4 * 4.5 = 3 * (DR)
What is DR?
3x = 4 * 4.5
Solve for x.
Can you do that?
The equation we have for your problem is the same, except the length of the segment DR was used instead of x.
4 * 4.5 = 3 * (DR)
18 = 3(DR)
3DR = 18
DR = 6
Now notice that chord BD passes through the center of the circle, point P, so chord BD is a diameter. The length of diameter BD is the sum of the lengths of segments BR, 3, and DR, 6.
Once you know the diameter of the circle, you can find the circumference of the circle and the area of the circle.
\(\large C = \pi d = 2 \pi r\)
\(\large A = \pi r^2\)
Use the diameter multiplied by pi to find the circumference of the circle.
Then divide the diameter by 2 to find the radius. Square the radius and multiply by pi to find the area.