Question

Question 1.

A circle has a center point upper C. Points upper D, upper E, upper F and upper G lie on the circumference of the circle.

If CH=42 m and CF=58 m, then what is the length of FG?

(1 point)
Responses

80 m
80 m

32 m
32 m

16 m
16 m

40 m
40 m
Question 2
Question 2.

A circle has center point upper O. Upper O connects to a point on the circumference labeled upper B. Upper B connects to a point outside the circle labeled upper A. A diagonal line connects upper A and upper O to form the shape of a triangle.



If BO=45 in. and BA=108 in., then what is the length of AO to the nearest whole inch?

(1 point)
Responses

98 in
98 in

117 in
117 in

25 in
25 in

67 in
67 in
Question 3
Question 5.

Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.



The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <A.

(1 point)
Responses

98°
98°

82°
82°

106°
106°

53°
53°
Question 4
Question 10.

If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle? Leave your answer in terms of π.

(1 point)
Responses

2025π8 mm

2025π8 mm


75π4 mm

75π4 mm


54π mm

54π mm


75π8 mm

75π8 mm

Question 5
Question 11.

What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches? Leave your answer rounded to the nearest tenth.

(1 point)
Responses

29.4 inches
29.4 inches

26.4 inches
26.4 inches

13.2 inches
13.2 inches

92.4 inches
92.4 inches
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Answer 1

Here are the answers with brief work:

1) 80 m.
- CH is the perpendicular distance from center to chord FG, CF = radius = 58. FG = 2√(58^2 − 42^2) = 2√1600 = 80.

2) 117 in.
- BA is tangent at B, so ∠ABO = 90°. AO = √(AB^2 + BO^2) = √(108^2 + 45^2) = 117.

3) 82°.
- ∠A intercepts arc BD = arc BC + arc CD = 58° + 106° = 164°. So ∠A = 1/2·164° = 82°.

4) 75π/4 mm.
- Arc length = r·θ (radians) = 27·(125°·π/180) = 27·(25π/36) = 75π/4.

5) 92.4 (in^2).
- Sector area = (216/360)·π·7^2 = (3/5)·π·49 = (147/5)π ≈ 92.4.