I drew the 12 cm chord at the end of a radius, giving me an isosceles triangle with sides 20,20 and 12
Define the "two regions" created.
In a circle with radius 20cm, a chord is drawn with length 12 cm.
Find the area of the two regions created.
Find the perimeter of the two regions created.
2 answers
Hmmm. Isn't every chord drawn at the end of a radius?
Any chord divides the circle into two regions.
The area of the segment is the area of the sector less the area of the triangle, or r^2/2 (θ - sinθ)
sin θ/2 = 6/20, so θ/2 = .3047
sinθ = .5723
The area of the segment is thus 200*(.6094-.5723) = 7.42
So, the rest of the circle has area 400π - 7.42 = 1249.2171
arc length subtended by chord: rθ = 20*.6094 = 12.188
other arc is 2πr - rθ = 40π - 12.188 = 113.476
so, the perimeters are arc length + chord length = 24.188 and 125.476
(assuming no stupid arithmetic errors)
Any chord divides the circle into two regions.
The area of the segment is the area of the sector less the area of the triangle, or r^2/2 (θ - sinθ)
sin θ/2 = 6/20, so θ/2 = .3047
sinθ = .5723
The area of the segment is thus 200*(.6094-.5723) = 7.42
So, the rest of the circle has area 400π - 7.42 = 1249.2171
arc length subtended by chord: rθ = 20*.6094 = 12.188
other arc is 2πr - rθ = 40π - 12.188 = 113.476
so, the perimeters are arc length + chord length = 24.188 and 125.476
(assuming no stupid arithmetic errors)
4 answers