Basic Terminology Central Angle: An angle in the center of a circle Arc: A portion of a circle Arc.

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Presentation transcript:

Basic Terminology Central Angle: An angle in the center of a circle Arc: A portion of a circle Arc

Basic Relationships Arcs and Central Angles have the same measure. 65

More Basic Terminology Major & Minor Arcs: Major arcs are between 180 and 360 degrees. Minor arcs are between 0 and 180 degrees. Naming Arcs: Minor arcs are named using 2 letters, while a major arc is named using 3 letters. This is done to avoid confusion. Minor Arc = AB Major Arc = ACB Minor Arc Major Arc A C B

Finding the Length of an Arc Step 1:Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 5 cm Circumference = πd so… C= π(10)= 10π The arc takes up 90/360 degrees or ¼ of the circle.

Finding the Length of an Arc Step 1:Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 8 cm Circumference = πd so… C= π(16)= 16π The arc takes up 120/360 degrees or 1/3 of the circle. 120 pi formdecimal form 240 We’re missing the angle in the red arc.

Finding the Length of an Arc Step 1:Find the length around the entire circle (Circumference = πd). Step 2: Figure out what fraction of the whole circle the arc take up. (Hint: use 360) Step 3: Multiply the circumference by the fraction for the arc. 4 cm Circumference = πd so… C= π(10)= 8π The arc takes up 130/360 degrees. I’m not sure what nice fraction that is. 130 pi formdecimal form

Area of a Sector What is a sector? A sector is like a pizza slice. It is part of the area of a circle.

Finding the Area of a Sector Step 1:Find the area of the entire circle (Area= πr 2 ). Step 2: Figure out what fraction of the whole circle the sector takes up. (Hint: use 360) Step 3: Multiply the area by the fraction for the sector. 4 cm Area= πr 2 so… Area= π4 2 = 16π The sector takes up 130/360 degrees. I’m not sure what nice fraction that is. 130 pi formdecimal form

Finding the Area of a Sector Step 1:Find the area of the entire circle (Area= πr 2 ). Step 2: Figure out what fraction of the whole circle the sector takes up. (Hint: use 360) Step 3: Multiply the area by the fraction for the sector. 3 cm Area= πr 2 so… Area= π3 2 = 9π The sector takes up 240/360 degrees. 120 pi formdecimal form

Finding the Area of Segments What is a segment? The space between a line connecting two points of a circle and the circle itself.