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The chapter covers the concepts of sectors and segments of a circle, including the formulas needed to calculate their areas and the lengths of arcs. It provides detailed explanations of how to derive the area of a sector based on its angle and radius, and also discusses the relationship between the areas of segments and their corresponding triangles. Various examples reinforce the application of these concepts in solving problems relevant to circles.
Chapter 113 sections
The chapter covers the concepts of sectors and segments of a circle, including the formulas needed to calculate their areas and the lengths of arcs. It provides detailed explanations of how to derive the area of a sector based on its angle and radius, and also discusses the relationship between the areas of segments and their corresponding triangles. Various examples reinforce the application of these concepts in solving problems relevant to circles.
Length of an arc of a sector of a circle with radius r and angle with degree measure θ is θ/360 × 2πr.
Area of a sector of a circle with radius r and angle with degree measure θ is θ/360 × πr².
Area of a segment of a circle = Area of the corresponding sector - Area of the corresponding triangle.
A sector of a circle is a portion enclosed by two radii and the arc between them.
A segment of a circle is the area enclosed by a chord and the arc connecting the endpoints of the chord.
The distance along the arc connecting two points on the circle, calculable using the arc's angle and radius.
The area of a sector can be calculated using the formula (θ/360) × πr².
Total Questions
2
Estimated Time
4 min
Passing Score
70%
3 more questions available