Area of a Sector of a Circle Three circles with radii 1, 2, and 3 ft are externally tangent to one another, as shown in the figure. Find the area of the sector of the circle of radius 1 that is cut off by the line segments joining the center of that circle to the centers of the other two circles.
The area of sector is .
The radius of circle
Before applying the formula for area of sector we need to find the central angle theta which the sector subtends.
As, shown in the figure
Applying Pythagoras theorem
Also, the area of sector is given by
Putting the values of Ab, BC and AB in Pythagoras Theorem we find the central angle of the sector as .
Therefore the area of sector is:
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