Are all the radii of a circle equal in length?

By the definition of a circle, any two radii have the same length. Since a diameter consists of two radii joined at their endpoints, every diameter has length equal to twice the radius. Hence, all radii of a circle are equal.

Which circles do have the same length of radius?

Congruent circles are circles that have the same radius but different centers. Concentric circles are two circles that have the same center, but a different radii. Intersecting Circles: Two circles may intersect at two points or at one point.

What is the length of radii of a circle?

The definition of radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. So, the radius is half the length of the diameter.

Do all circles have the same size?

But the size of a circle may vary. Thus circles are similar. Each circle has a different radius so the size of the circle may vary. .

Are two circles always similar?

Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (they only vary by size), any circle can be scaled to form any other circle. Thus, all circles are similar!

What is the relationship between the length of a radius and the length of a diameter?

The diameter of a circle is twice the length of the radius, so the radius is half the length of the diameter.

What is twice the radius?

By extension, the diameter D is defined as twice the radius: If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere.

Why must all circles be similar?

Because the size of any circle is defined by its radius, we use the radii to determine its scale factor. Since a radius is a constant (an unchanging number), and any constant is proportional to another constant, then all circles must be similar.

Why are all circles similar proof?

Because a circle is defined by its center and radius, if two circles have the same center and radius then they are the same circle. This proves that in general, all circles are similar.

What is the relationship between radius and circumference?

The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius.