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Understanding Circle Geometry: Circumference, Arc Length, and Angle Formulas

This educational resource focuses on key concepts of circle geometry including the formulas for inscribed angles, vector relationships outside circles, and calculations for circumference and arc length. It features various examples demonstrating how to find the circumference of circles with given radii and diameters, as well as methods for calculating exact arc lengths and areas of sectors and segments. The material also covers angle measurement conversions between degrees and radians. Ideal for students preparing for EOCT Week 14.

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Understanding Circle Geometry: Circumference, Arc Length, and Angle Formulas

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

  2. EOCT Week 14 #4

  3. Circumference & Arc Lengthof Circles

  4. Circumference The distance around a circle

  5. Circumference or

  6. r = 14 feet d = 15 miles Find the EXACT circumference.

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

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

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

  10. Arc Length

  11. Ex 6. Find the Arc LengthRound to the nearest hundredths 8m  70

  12. Ex 7. Find the Arc Length Round to the nearest hundredths 12 in  110

  13. Ex 8. Find the exact Arc Length.

  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: Mode – RAD Type degrees Math – DMS – 1: ORAngle – 1: enter Mode – DEG Type radians Math – DMS – 4: OR Angle – 4: enter

  25. Arc Length Homework 11 problems

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