Basic Geometry : How to find the length of the diameter

Example Questions

Example Question #341 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #342 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #343 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #344 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #345 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #351 : Circles

Find the length of the diameter of a circle inscribed in a square that has a diagonal of .

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

Substitute in the length of the diagonal to find the length of the square.

Simplify.

Now, recall the relationship between the diameter of the circle and the side of the square.

Example Question #352 : Circles

Find the length of the diameter given the area is .

Explanation:

To solve, simply use the formula for area to solve for the radius and multiply by 2.

Example Question #353 : Circles

The circumference of a circle is equal to . Find the length of the diameter of this circle.

Explanation:

There are two steps to finding the answer to this question. The first is to find the radius through the formula for the circumference of a circle.

Then we plug in numbers and solve.

Now that we have found the radius, we solve for diameter by doubling it, since..

Therefore, the diameter is equal to

Example Question #354 : Circles

Find the length of the diameter given radius is 7.

Explanation:

To solve, simply use the formula for the diameter of a circle.

Recall that the diameter of a circle is twice the radius of the circle.

Given that the radius is seven, multiply it by 2 to solve for the diameter.

Thus,

.

Example Question #355 : Circles

Find the length of the diameter of a circle given an area of  .