HS.G.18(+).a: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius. Derive the formula for the area of a sector.

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius. Derive the formula for the area of a sector.

Example Problems
An arc subtends a central angle of radians. What fraction of the circumference is the arc?
An arc subtends a central angle of radians. What fraction of the circumference is the arc?
An arc subtends a central angle of radians. What fraction of the circumference is the arc?
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