Arc Length, Sector Area, and Inscribed Angles

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Presentation transcript:

Arc Length, Sector Area, and Inscribed Angles Ms. Mougharbel

Definitions Arc Length: Length of an arc (not degree) Sector: he part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle Inscribed Angle Theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle

Sector Area Inscribed Angle Theorem

Formulas Area of a sector: 𝐴= 𝐴𝑟𝑐 𝐷𝑒𝑔𝑟𝑒𝑒 360 (𝜋 𝑟 2 ) Length of an arc: 𝐿= 𝐴𝑟𝑐 𝐷𝑒𝑔𝑟𝑒𝑒 360 (2𝜋𝑟)