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Problem 610

# Inscribe a square in a circle.

Expert verified
To inscribe a square in a circle with radius r, find the side length of the square using the Pythagorean theorem as $$s=\sqrt{2r^2} = r\sqrt{2}$$. Draw the square with its vertices at the points (±r/√2, ±r/√2) on a coordinate plane with the circle's center at the origin. The square will be inscribed in the circle with each vertex touching the circumference.
See the step by step solution

## Step 1: Find the radius of the circle

Let the circle have radius r.

## Step 2: Use Pythagorean theorem to find the side of the square

We know that the diagonal of the square is equal to the diameter of the circle, which is 2r. Let the side of the square be s, then using the Pythagorean theorem, we can write: $$s^2 + s^2 = (2r)^2$$.

## Step 3: Simplify the equation and solve for s

Simplifying the equation, we get: $$2s^2 = 4r^2$$. Now, divide both sides by 2: $$s^2=2r^2$$. Then take the square root of both sides to find the side length of the square: $$s=\sqrt{2r^2} = r\sqrt{2}$$.

## Step 4: Draw the square inside the circle

To draw the square inside the circle: 1. Place the center of the circle at the origin (0,0) on the coordinate plane. 2. Draw the square with its vertices at the points (±r/√2, ±r/√2). The square is now inscribed in the circle with each vertex touching the circumference of the circle.

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