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n In a circle of radius r, the length l of an arc of measure n equals of the circumference 360 pnr n of the circle, or l . 2pr 360 180 n In a circle of radius r, the area K of a sector of measure n equals of the area of the 360 n 2. circle, or K pr 360 Area of a sector of n Area of the circle length of an arc of measure n circumference of the circle n 360

PRINCIPLE 3: PRINCIPLE 4:



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The area of a minor segment of a circle equals the area of its sector less the area of the triangle formed by its radii and chord. If a regular polygon is inscribed in a circle, each segment cut off by the polygon has area equal to the difference between the area of the circle and the area of the polygon divided by the number of sides.

Amount 850 800 1,200 1,650 900 1,600 7,000

PRINCIPLE 5:

Table 5-2 Name appendChild(newChild)

10.11 Length of an arc (a) Find the length of a 36 arc in a circle whose circumference is 45p. (b) Find the radius of a circle if a 40 arc has a length of 4p.

(a) Here n (b) Here l 36 and C 4p and n 2pr 45p. Then l n 2pr 360 36 9 45p p. 360 2 40 2pr, and r 360





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10.12 Area of a sector (a) Find the area K of a 300 sector of a circle whose radius is 12. (b) Find the measure of the central angle of a sector whose area is 6p if the area of the circle is 9p. (c) Find the radius of a circle if an arc of length 2p has a sector of area 10p.

10.13 Area of a segment of a circle (a) Find the area of a segment if its central angle measures 60 and the radius of the circle is 12. (b) Find the area of a segment if its central angle measures 90 and the radius of the circle is 8. (c) Find each segment formed by an inscribed equilateral triangle if the radius of the circle is 8.

1 2 4 s 23

n pr2 360 1 4 (144) 23

General Journal Date Description 12/22 Sales Returns Accounts Receivable 12/26 Sales Returns Accounts Receivable

60 144p 360 36 23.

24p.

1 2 bh 1 2 (8)(8)

32. 48 23.

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1 (c) R 8. Since s R 23 8 23, the area of ^ABC is 4s2 23 Also, area of circle O pR2 64p. 1 Hence, area of segment BDC 3(64p 48 23).

Fig. 10-11

7

10.14 Area of a segment formed by an inscribed regular polygon Find the area of each segment formed by an inscribed regular polygon of 12 sides (dodecagon) if the radius of the circle is 12. (See Fig. 10-12.)

Fig. 10-12

n 30 pr2 144p 12p. 360 360 To find the area ^OAB, we draw altitude AD to base OB. Since m/AOB Area of sector OAB Then the area of ^OAB is

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1 2 bh 1 2 (12)

1 2r

(6) 36.

The areas of combination figures like that in Fig. 10-13 may be found by determining individual areas and then adding or substracting as required. Thus, the shaded area in the figure equals the sum of the aeas of the square and the semicircle: A 82 1(16p) 64 8p. 2

In This :

Fig. 10-13

10.15 Finding areas of combination figures Find the shaded area in each part of Fig. 10-14. In (a), circles A, B, and C are tangent externally and each has radius 3. In (b), each arc is part of a circle of radius 9.

Fig. 10-14

1 2 4 s 23

9 23 182 324

1 2 (6 ) 23 9 23. Area of sector I 4 15 3 A 2 pR 9 23 45p. 2 n (pr2) 360

Introduction Cash Receipts Journal Cash Disbursements Journal Combination Cash Journal Summary Solved Problems

n (pr2) 360

300 (9p) 360

15 p. 2

90 (81p) 360

81 p.1 4

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