# Basic Geometry : How to find circumference

## Example Questions

### Example Question #71 : How To Find Circumference

If a rectangle with a diagonal of  is inscribed in a circle, what is the circumference of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Substitute in the given diameter to find the circumference.

### Example Question #72 : How To Find Circumference

If a rectangle with a diagonal of  is inscribed in a circle, what is the circumference of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Substitute in the given diameter to find the circumference.

### Example Question #73 : How To Find Circumference

If a rectangle with a diagonal of  is inscribed in a circle, what is the circumference of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Substitute in the given diameter to find the circumference.

### Example Question #74 : How To Find Circumference

If a rectangle with a diagonal of  is inscribed in a circle, what is the circumference of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Substitute in the given diameter to find the circumference.

### Example Question #75 : How To Find Circumference

If a rectangle with a diagonal of  is inscribed in a circle, what is the circumference of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Substitute in the given diameter to find the circumference.

### Example Question #76 : How To Find Circumference

Given that the radius of a circle is , solve for the circumference.

Explanation:

The circumference of a circle is found by using the following formula:

Plug in the radius from the given information, and you get this:

### Example Question #77 : How To Find Circumference

Find the circumference of a circle given the radius is 3.

Explanation:

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

Given that the radius is 3, substitute 3 in for the r in the circumference formula below.

Thus,

.

### Example Question #77 : How To Find Circumference

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the hypotenuse.

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

Simplify.

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

Now, recall how to find the circumference of a circle:

Substitute in the value for the diameter to find the circumference of the circle.

### Example Question #261 : Radius

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the hypotenuse.

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

Simplify.

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

Now, recall how to find the circumference of a circle:

Substitute in the value for the diameter to find the circumference of the circle.

### Example Question #79 : How To Find Circumference

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the hypotenuse.

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

Simplify.

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

Now, recall how to find the circumference of a circle:

Substitute in the value for the diameter to find the circumference of the circle.