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Section 7.5 More Area Relationships in the CirclePowerPoint Presentation

Section 7.5 More Area Relationships in the Circle

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Section 7.5 More Area Relationships in the Circle

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Sector of a circle is a region bounded by two radii of the circle and an arc intercepted by those radii.

Segment of a circle is a region bounded by a chord and its minor (or major) arc.

Section 7.5 Nack

- Postulate 23: The ratio of the degree measure m of the arc (or central angle) of a sector to 360 is the same as the ratio of the area of the sector to the area of the circle:
area of sector = m

area of circle 360

- Theorem 7.5.1: In a circle of radius r, the area A of a sector whose arc has degree measure m is given by:
A = m r²

360

- Corollary 7.5.2: The area of a semicircular region of radius r is A = ½r²
Example 1-3 p. 373-4

- Corollary 7.5.2: The area of a semicircular region of radius r is A = ½r²

Section 7.5 Nack

- Area of a Segment is the area of the sector minus the area of the triangle formed using the center of the circle and the endpoints of the sector.
Asegment = Asector – AΔ

Asegment = 90 12² - ½ 1212

360

=(36 - 72) square units.

12

12

Section 7.5 Nack

- Theorem 7.5.3: Where P represents the perimeter of a triangle and r represents the length of the radius of its inscribed circle, the area of the triangle is given by:
A = ½rP

Section 7.5 Nack