In circle O, if chord $AE$ has length $7$ units and passes through the center O, what is the radius of the circle?

• A. $7$ units
• B. $\frac{7}{2}$ units
• C. $14$ units
• D. $3.5$ units

Answer: (A)

Verified step by step guidance

1. Understand that the chord AE passes through the center O of the circle, which means AE is a diameter of the circle.
2. Recall that the diameter of a circle is twice the radius, so we can write the relationship as \(\text{Diameter} = 2 \times \text{Radius}\).
3. Given the length of chord AE (which is the diameter) is 7 units, set up the equation \$7 = 2r\(, where \)r$ is the radius.
4. Solve for the radius \(r\) by dividing both sides of the equation by 2, giving \(r = \frac{7}{2}\).
5. Conclude that the radius of the circle is \(\frac{7}{2}\) units.