# Circle question

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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.

• Circle question -

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.

• Circle question -

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)

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