8/18/2019 Exercise Chapter 8

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1. 

O A B

C 

13 cm

5.2 cm

 

The figure shows the sector OCB of radius 13 cm at the center O. The length of the arc

CB = 5.2 cm. Find

a.  The angle in radians.

 b. 

The perimeter of the shaded region.

2. 

O A

 B

   5  c  m

5 cm

6 cm

 

The figure shows the sector  AOB of a circle, center O and radius 5 cm. The length of the

arc  AB is 6 cm. Find the area of

a.  The sector  AOB.

 b.  The shaded region.

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3.  Diagram below shows a sector QOR of a circle with center O.

1.75 rad

O

 P 

Q

 RS 

 

It is given that  PS  = 8 cm and QP  =  PO = OS  = SR = 5 cm. Find

a.  The length, in cm, of the arc QR.

 b.  The area, in cm2, of the shaded region.

4.  Diagram below shows a circle with center O.

O

 A

 B

ϴ

The length of the minor arc is 16 cm and the angle of the major sector  AOB  is 290°.

Using π = 3.142, find

a.  The value of ϴ, in radians.

 b.  The length, in cm, of the radius of the circle.

8/18/2019 Exercise Chapter 8

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8/18/2019 Exercise Chapter 8

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7.  Diagram shows a circle, center O and radius of 8 cm inscribed in a sector SPT  of a circle

at center  P . The straight lines, SP  and TP , are tangents to the circle at point Q and point  R,

respectively.

S 

Q

T 

 R

O

 P 

60°

8 cm

 

Calculate

a.  The length, in cm, of the arc ST .

 b.  The area, in cm2, of the shaded region.

8.  Diagram below shows two circles. The larger circle has center  A and radius 20 cm. The

smaller circle has center  B and radius 12 cm. The circles touch at point  R. The straight

line  PQ is a common tangent to the circles at point  P  and point Q.

Q

 P 

 A

 B

 R

12 cm

20 cm

ϴ

Given that ⦟ PAR = ϴ radians,

a.  Show that ϴ = 1.32.

 b.  Calculate the length, in cm, of the minor arc QR.

c.  Calculate the area, in cm2, of the shaded region.

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9.  Diagram below shows a circle  PQRT , center O and radius of 5 cm.  AQB  is a tangent to

the circle at Q. The straight lines,  AO and  BO, intersect the circle at  P  and  R respectively.

OPQR is a rhombus.  ACB is an arc of a circle at center O.

O

 A B

C 

 P Q R

T 

 x rad

 

Calculate

a. 

The angle  x, in terms of π. b.  The length, in cm, of the arc  ACB.

c. 

The area, in cm2, of the shaded region.

10. 

 A B

 X 

Y 

 P 

O

ϴ

10 cm

5 cm

0.82 rad

 

In the diagram above,  AXB  is an arc of a circle center O  and radius of 10 cm with

⦟ AOB = 0.82 radian.  AYB is an arc of a circle center  P  and radius of 5 cm with ⦟ APB =

ϴ. Calculate

a.  The length of the chord  AB.

 b.  The value of ϴ in radians.

c.  The differences in length between the arcs  AYB and  AXB.