I'm trying to figure out the length of a side of a square:
I tried to work it out this way:A square is inscribed in a circle of radius r. Express the length of the side of the square in terms of r.
since the the lines insribed on the insides of a square are right angles right?
but the answer says r doesn't = x so what am I doing wrong here and how can I get the right answer?
I interpreted it this way.
A square is inscribed in a circle of radius r. Express the length of the side x of the square in terms of r.
Draw r from the center of the circle to a vertex on the square.
Drop a perpendicular from the center of the circle to the side of the square.
You have formed a 45-45-90 triangle with r as the hypotenuse.
If x represents a side of the square, then x/2 will represent the sides of the isosceles triangle.
Use the Pythagorean Theorem to represent r in terms of x.