Lesson Component 4 (Lesson Activity)
Time: 25 minutes
Part 4A
Stem for Items 1 and 2
C
N
E
F
K
K
L
M
B
D
A
A large park Includes a circular area of radius 50 meters and a number of pathways that cross the area, as well as
two pathways
that are tangent to the area. Sebastian works for the council that manages the park and needs to
check various measurements in relation to the circular park area for an upcoming project.
Sebastian knows that the circular park area, having a 50-meter radius, has an area of 2500 square meters and a
circumference of 100 meters.
As part of the upcoming project, it is proposed that a new pathway AN (shown as a broken line) be constructed.
Part 4B
Item 1
Questions
1. (1) Show that the central reflex angle EOF measures 288°.
(ii) In the diagram, the central angle EOF stands on the same arc EF as the inscribed angle EDF.
Sebastian has measured ZEOF to be 72°. What measurement should he obtain for
between pathways DE and DF?
EDF, the angle
2. (i) Given that the circular park area has a circumference of 100 meters and an area of 2500 square
meters, calculate the length of the arc EF and the area of the minor sector EOF.