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 More Area Relationships in the Circle. Area of a Sector.

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Section 7 5 more area relationships in the circle

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 7.5More Area Relationships in the Circle

Section 7.5 Nack


Area of a sector
Area of a Sector circle and an arc intercepted by those radii.

  • 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 = ½r²

      Example 1-3 p. 373-4

Section 7.5 Nack


Area of a segment
Area of a Segment circle and an arc intercepted by those radii.

  • 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 1212

    360

    =(36 - 72) square units.

12

12

Section 7.5 Nack


Area of a triangle with an inscribed circle
Area of a Triangle with an inscribed circle circle and an arc intercepted by those radii.

  • 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


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