# Length of the Diameter of a Circle

The length of the diameter of the circle is equal to .

Consider the equation of a circle is given by

Let be the point of the circle. By putting this point in a circle, then

Since the origin is the center of the given circle (i), the line through and across the circle is its diameter. The equation of the line through and using two points from the line is

Putting the value of from equation (iii) in equation (i), we have

Putting in the above equation (iii), we have . This shows that the other end of the diameter is , as shown in the given diagram. Now the length of the diameter is

This is the required result.