Question

In circle I, IJ = 2 and the area of shaded sector = . Find the length of JLK.

Express your answer as a fraction times T.
J
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Answer 1

Given that IJ = 2, we know that IJ is the radius of the circle.

The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:

(x/360) * pi * 2^2 =

Solving for x:

x = (180/pi)*

We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.