1. 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.
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2. Area of a Sector
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 
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
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3. Area of a Segment
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
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4. Area of a Triangle with an inscribed circle
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
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Section 7.5 Nack