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.
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Warm Up April 24th 1. What is the formula for the inscribed angle? 2. What is the formula for a vector outside the circle?
Circumference & Arc Length of Circles
Circumference The distance around a circle
Circumference C C 2 r d = = or
Find the EXACT circumference. 1. r = 14 feet 28 ft 2. d = 15 miles 15 miles
Ex 3 and 4: Find the circumference. Round to the nearest tenths. 14.3 mm 33 yd 89.8 mm 103.7 yd
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
Arc Length The distance along the curved line making the arc (NOT a degree amount)
Arc Length measure of arc 360 = 2 Arc Length r
Ex 6. Find the Arc Length Round to the nearest hundredths measure of arc 360 = 2 Arc Length r 8m 70 9.77 m
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
Ex 8. Find the exact Arc Length. measure of arc 360 = 2 Arc Length r 10 3 in
Ex 9. Find the exact area of the circle.
Ex 10. Find the exact area of the circle.
Ex 11. Find the exact area of the sector of the circle.
Ex 12. Find the exact area of the sector of the circle.
Ex 13. Find the area of the segment.
Ex 14. Find the area of the segment.
Radian Measure of a Circle another way to measure angles!
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
Arc Length Homework 11 problems
