SOLUTION: A decorative dinner plate is displayed in a V-shaped rack as shown. The radius of the plate is 7 inches. The measure of angle APC = 50 degrees. The sides of the rack form tangents

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Question 147999: A decorative dinner plate is displayed in a V-shaped rack as shown. The radius of the plate is 7 inches. The measure of angle APC = 50 degrees. The sides of the rack form tangents to the plate.

A decorative dinner plate is displayed in a V-shaped rack as shown. The radius of the plate is 7 inches. The measure of angle APC = 50 degrees. The sides of the rack form tangents to the plate.
a) Find the circumference of the plate.
b)Find the measure of angle PAB. Explain how you found the measure.
c)Find the measure of minor arc AC and major arc ADC. Explain how you found the measure
d)Use the circumference of the circle that you found in part a to find the length of arc AC. Explain your answer.
Answer by mangopeeler07(462) (Show Source):
You can put this solution on YOUR website!
A decorative dinner plate is displayed in a V-shaped rack as shown. The radius of the plate is 7 inches. The measure of angle APC = 50 degrees. The sides of the rack form tangents to the plate.
a) Find the circumference of the plate.

b)Find the measure of angle PAB. Explain how you found the measure.

*This depends on the placement of B, which is not identifiable given the question alone. You probably have a diagram. If you can describe where B is located on the circle, I can help you find this angle.

c)Find the measure of minor arc AC and major arc ADC. Explain how you found the measure

If the center of the circle is P, then APC is a central angle. Therefore its arc, AC, is the same measure as the angle. angle APC = 50 degrees, therefore arc AC=50 degrees.

d)Use the circumference of the circle that you found in part a to find the length of arc AC. Explain your answer.

How much of the circumference is 50 degrees?

Cross multiply:

Divide by 360