Question

Fill in the blanks:

The longest chord of a circle is a ______ of the circle.

• A. Diameter
• B. Secant
• C. Radius
• D. none of the above

Answer 1

The correct option is A Diameter

Let AB be a diameter of the circle with center C and DE a chord not through C. Then, by the definition of the circle as the locus of points equidistant from the center, CA=CB=CD=CE=R, the radius of the circle. Which makes AB=2R. (The diameter is twice as long as the radius.)

On the other hand, in CDE, by the triangle inequality,

DE<CD+CE=R+R=2R=AB.
Hence Diameter is the longest chord