# Section 7.5 More Area Relationships in the Circle - PowerPoint PPT Presentation

1 / 4

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Section 7.5 More Area Relationships in the Circle

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

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

### 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 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 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

• 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