Math 2
G.C.2, G.C.5 (L1-7)
Assessment Title: It’s a Circular Life
Unit 9: Circles
Learning Target:
 Apply relationships among central angles, inscribed angles, circumscribed angles, radii, chords
and tangents to determine the measures of arcs and angles in a circle.
1.
A regulation dartboard is divided into twenty equal-sized sectors for the twenty numbers. The
chart below indicates the distance from the center of the dartboard for each ring possible on the
board. So, for example, the inside of the triple ring is 3.75 inches from the center and the outside
of that ring is 4.125 inches from the center.
Distance (in inches)from
center of dartboard
Greater than Less than
0
0.25
0.25
0.625
0.625
3.75
3.75
4.125
4.125
6.25
6.25
6.625
a.
b.
Dart will land in:
Inner Bull(seye)
Outer Bull(seye)
Single Score
Triple Ring
Single Score
Double Ring
For any one of the twenty
numbers, what is the area of the following scoring region on a regulation dartboard?
i.
Triple Ring
ii.
Double Ring
iii.
Single Score
For any one of the twenty numbers, what is the perimeter of its Single Score region
on a regulation dartboard?
c. For any value (1 to 20), the triple ring is worth 3/2 as many points as the double ring. Is
this fair given the respective areas of each of those regions? Explain your answer
and provide the supporting mathematics.
d.
(Extension) If a dart is randomly thrown so that it lands in the Play Area, what is the
probability that it lands in the following scoring region.
i.
Triple Ring for the number 20
ii.
Double Ring for the number 5
iii.
Single Score
iv.
Outer Bull(seye)
10. Making a fair dartboard. Suppose you were going to make a simple dartboard with just an outer
ring and an inner ring. If the radius of the large circle (outer ring) is 6 inches,
a. How large should the radius of the inner circle be so that the areas (and thus the point values) for
each region would be the same:
b. In this case, how much larger is the circumference of the outer circle than the circumference of the
inner circle?
c. How large should the radius of the inner circle be so that the point values of the outer ring would be
twice the value of the inner ring:
d. How large should the radius of the inner circle be so that the point values of the outer ring are a
factor of b times the values of the inner ring?
11. Making a generalized fair dartboard. Suppose you were going to make a simple dartboard with just
an outer ring and an inner ring. If the radius of the large circle (outer ring) is R inches, how large should
the radius of the inner circle be so that the point values of the outer ring are a factor of b times the
values of the inner ring.