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maths b help

need help,can anyone solve dis question for me
The length of the minor arc AB of a circle is 2pi cm and the major arc is 22pi cm.Find
a) the radius of the circle
b) the acute angle AOB
Reply 1
Avatar for Robbie242
Robbie242
You know that you work out the length of minor and major arcs using the formula: l=rθl=r\theta where L is the length of the arc, r is the radius and θ\theta is the angle of the arc.

Lets suppose a minor arc of the circle is cut out (as it has told us) it will have an angle theta so we can say rθ=2πr\theta=2\pi
The major arc is everything left over, so we can say r(2π−θ)=22πr(2\pi-\theta)=22\pi (as 2π2\pi is the entire angle of the circle)

Solve r(2π−θ)=22πr(2\pi-\theta)=22\pi and rθ=2πr\theta=2\pi simultaneously to work out the values of r and theta (theta is the acute angle AOB)

Or actually if the length of the minor arc is 2pi and the major arc is 22pi then we can say the length of the entire circle will satisfy 24π=r2π24\pi=r2\pi ⇒r=12\Rightarrow r=12 and then theta can be worked out with relative ease
(edited 10 years ago)
Reply 2
Avatar for Tiger Rag
Tiger Rag
22
Moved to Maths

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