SOLUTION: Find the area in square centimeter of the largest square that can be cut from a sector of a circle radius 8 cm and a central 120 degree?

Question 1116522: Find the area in square centimeter of the largest square that can be cut from a sector of a circle radius 8 cm and a central 120 degree?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let A and B be the points on circle O with radius 8 such that angle AOB is 120 degrees.

Let the square be CDEF, with C on radius OA and D on radius OB.

Let OG be the radius that bisects the square and the 120 sector of the circle, intersecting CD at H and EF at I.

Let the side of the square be 2x, so that CH=HD=FI=IE=x.

We need to find the area of the square, which is .

In right triangle OHD, HD=x and angle D is 30 degrees, so .

In right triangle OIE, I is the right angle and the legs are and . Then since OE is a radius with length 8,

Answer: The area of the square is
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