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MODULE 5

REVIEW

Topic Topics Covered Pages

Topic A

Definition of a circle

Equation of a circle centered at the origin and not centered at the origin

2 – 3

Topic B

Angles of a circle- Central, inscribed, interior and exterior angles

4 – 6

Topic C

Finding the lengths of segments within circles and on the outside of the

circles

6 – 7

Topic D

Area of a Sector (Finding the area of a shaded region)

Finding the arc length (measure of a piece of the circumference)

8 – 10

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Determining the Center and Radius of a Circle:

1. Determine the center and radius of the given circle.

𝑥2 − 4𝑥 + 𝑦2 − 8𝑦 = 5

3

2. Determine the center and radius of the given circle. 2 28 2 8x x y y

3. Determine the center and radius of the given circle 2 26 20 12x x y y

4. Determine the center and radius of the given circle: 2 26 7 0x x y

5. A circle has a center at (5, 4) and radius of 6. Does the point (2.2, 1.3) lie on the circle? Justify your

answer.

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1. In the diagram to the right, BC is a diameter to circle A.Point D which is a

unique from points B and C, is plotted on circle A. Which statement must

always be true?

2.

3. In the accompanying diagram of circle O, 𝐴𝐵𝐶 ̂ = 260°. What is the m<ABC?

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1. In the diagram below of circle O with diameter BC and radius OA, chord DC is parallel to chord BA.

If 𝑚 < 𝐵𝐶𝐷 = 30, determine and state m<AOB.

2.

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3. In circle F, the measure of 𝑎𝑟𝑐 𝐶𝐵 = 60 and the measure of 𝑎𝑟𝑐 𝐴𝐷 = 40. Find the 𝑚 ∠𝐴𝐸𝐷

1. In circle O, secants ADB and AEC are drawn from external point A such that points D,B, E, and C are

on circle O. If 𝐴𝐷 = 8, 𝐴𝐸 = 6, and EC is 12 more than BD, the length of BD is

(1) 6

(2) 22

(3) 36

(4) 48

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2.

3.

4.

8

Area of a Sector

In Degrees:

𝐴 =𝜃

360∙ 𝜋𝑟2

𝜃 = central angle

𝑟 = radius

1. In the diagram below of circle 0, the area of the shaded sector AOC is 12𝜋 in2 and the length of 𝑂𝐴̅̅ ̅̅ is 6

inches. Determine and state 𝑚∠𝐴𝑂𝐶.

2. Triangle FGH is inscribed in circle O, the length of radius 𝑂𝐻̅̅ ̅̅ is 6, and 𝐹𝐻̅̅ ̅̅ ≅ 𝑂𝐺̅̅ ̅̅ .

What is the area of the sector formed by angle FOH? Leave in terms of 𝜋.

3. In the diagram below of circle O, the area of the shaded sector LOM is 2𝜋 cm2. If the length of NL is 6 cm,

what is the 𝑚∠𝑁?

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4. What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures

60°? Leave as a fraction and in terms of 𝜋

Arc Length

In radians:

𝑆 = 𝜃 ∙ 𝑟

S= Arc Length

𝜃 = central angle

𝑟 = radius

1.

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2.