SOLUTION: can you please help me solve ((( What is the area of a square inscribed in a circle with radius 6? )))

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Question 199048This question is from textbook geometry
: can you please help me solve ((( What is the area of a square inscribed in a circle with radius 6? )))This question is from textbook geometry

Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
The inscribed square has a diagonal equal to 2 times the radius ( or the diameter) of the circle and this is 2*6 = 12.
If a square has a diagonal of 12, then you can find the length of its sides by using the Pythagorean theorem:
Where c is the diagonal and, for a square, the two sides are equal and a = b, so...

Substitute c = 12 (the diameter of the circle).

Divide both sides by 2.

The area of the square with sides equal to a is:
Substitute
sq.units.