Circles: Formulas for Inscribed Angles and Circumference

Explore the formulas for inscribed angles, vectors outside the circle, and the circumference of a circle. Learn how to calculate the circumference using radius, diameter, or directly measure the arc length. Discover the relationship between arc length and the angle measure in a circle.

• Circles
• Formulas
• Inscribed Angles
• Circumference

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Uploaded on Aug 23, 2024 | 1 Views

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1. Warm Up April 24th 1. What is the formula for the inscribed angle? 2. What is the formula for a vector outside the circle?

2. EOCT Week 14 #4

3. Circumference & Arc Length of Circles

4. Circumference The distance around a circle

5. Circumference C C 2 r d = = or

6. Find the EXACT circumference. 1. r = 14 feet 28 ft 2. d = 15 miles 15 miles

7. Ex 3 and 4: Find the circumference. Round to the nearest tenths. 14.3 mm 33 yd 89.8 mm 103.7 yd

8. 5. A circular flower garden has a radius of 3 feet. Find the circumference of the garden to the nearest hundredths. 2 C= C 2 3 = r C = 18.85 ft

9. Arc Length The distance along the curved line making the arc (NOT a degree amount)

10. Arc Length measure of arc 360 = 2 Arc Length r

11. Ex 6. Find the Arc Length Round to the nearest hundredths measure of arc 360 = 2 Arc Length r 8m 70 9.77 m

12. Ex 7. Find the Arc Length Round to the nearest hundredths measure of arc 360 = 2 Arc Length r 12 in 110 23.04 in

13. Ex 8. Find the exact Arc Length. measure of arc 360 = 2 Arc Length r 10 3 in

14. Area of a Circle

15. Ex 9. Find the exact area of the circle.

16. Ex 10. Find the exact area of the circle.

17. Area of a sector of a circle

18. Ex 11. Find the exact area of the sector of the circle.

19. Ex 12. Find the exact area of the sector of the circle.

20. Area of a segment

21. Ex 13. Find the area of the segment.

22. Ex 14. Find the area of the segment.

23. Radian Measure of a Circle another way to measure angles!

24. How to convert from Degrees to Radians: Radians to Degrees: 180 multiply by multiply by 180 Mode RAD Type degrees Math DMS 1: OR Angle 1: enter Mode DEG Type radians Math DMS 4: OR Angle 4: enter

25. Arc Length Homework 11 problems