# Basic Geometry : How to find circumference

## Example Questions

### Example Question #281 : Circles

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.

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 #91 : 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.

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 #93 : 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.

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 #94 : 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.

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 #91 : 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.

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 #96 : 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.

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 #91 : 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.

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 #91 : 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.

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 #91 : 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.

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 #291 : 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.

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.