posted by Jennfier on .
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.
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.
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)