Circle Unit Chapter 9

Definitions A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. A radius (plural, radii) is a segment from the center of the circle to a point on the circle. A chord is a segment whose endpoints lie on a circle. A diameter is a chord that contains the center of a circle. A central angle is an angle formed by two rays originating from the center of a circle (2 radii) An arc is an unbroken part of a circle (along the circumference)

All the parts to a circle…

3 types of Arcs Semicircle: endpoints are the endpoints of a diameter Usually use 3 letters to write the name of a semicircle Ex: 𝑀𝑂𝑁 , 𝑁𝐿𝑀 Minor Arc: shorter than a semicircle Usually use 2 letters to write the name of a minor arc Ex: 𝑀𝑂 , 𝐿𝑀 Major Arc: longer than a semicircle Usually use 3 letters to write the name of a major arc Ex: 𝑀𝐿𝑂 , 𝑁𝑀𝐿

Intercepted Arc: An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle.

Measuring Arcs in Terms of Degrees Semicircle = 180 because it is half of the distance around the circle 𝐴𝐶𝐵 =180° Minor Arc = measure of its central angle 𝐶𝐵 =35° Major Arc = 360 - measure of its minor arc 𝐶𝐷𝐵 =360°−35°=325°

Practice Find m 𝐴𝐶 Find m 𝐴𝐵𝐶

“Prizes” 10 tickets = 1 point on test/project (f/ Q4) 30 tickets = 100 homework grade 40 tickets = 100 quiz grade 150 tickets = 100 test/project grade 1-9 tickets left over = 2 pieces of candy