radius of the Circumscribing Circle, Length of Arc, and Sector
1. Solutions to the THQ
Collegeof EngineeringandComputerStudies,
St. Michaelβs College
Iligan City
2. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
1. The sides of a triangle are 80 cm, 100 cm, and 140 cm.
Determine the radius of the circumscribing circle.
π =
πππ
4π΄
; π =
80 + 100 + 140
2
ππ = 160 ππ
π =
80 100 140
4 160 160 β 80 160 β 100 160 β 140
ππ
=
175 6
6
ππ β 71.44 ππ
3. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
2. A central angle of 136β¦ subtends an arc of 28.5 cm.
What is the radius of the circle?
π = ππ βΉ π =
π
π
π = 136Β°
π
180
=
34π
45
πππ.
Hence,
π =
π
π
=
28.5 ππ
34π
45
β 12.01 ππ
4. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
3. Each of the four circles shown in the figure is tangent to the other
three. (a) If the radius of each of the smaller circles is π, find the
area of the largest circle. (b) If π = 2.71 cm what is the area of
the largest circle?
5. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
Solution: (a)
Triangle OMN is an equilateral triangle.
Hence, β πππ = 30Β°.
Consider βΏπππ:
cos 30Β° =
π
β
β β =
π
cos 30Β°
.
The radius of the big circle is:
π = π + β = π +
π
cos 30Β°
6. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
Solution: (b)
The radius of the big circle is:
π = π + β = π +
π
cos 30Β°
If π = 2.71 cm.
π΄ = ππ2
π΄ = π 2.71 +
2.71
cos 30Β°
2
ππ.2
π΄ = 107.12 ππ.2
7. Collegeof EngineeringandComputerStudies, St. Michaelβs College, Iligan City
4. Each of the four quarter arcs shown in the figure
measures 16 ft. in length. Find the area of the light
shaded region.
π΄ =
1
2
ππ ; 4 16 = 2ππ βΉ π =
32
π
ππ‘.
Area of the light shaded region
= Area of the 4 squares β Area of the 4 sectors
= 4
32
π
2
β 4
1
2
32
π
2
sq. ft
=
2048
π2 sq.ft
β 207.51 sq. ft