Which statement is TRUE only for some cases? A. if the diameterof a circle is an irrational number,then the radius of this circle is also an irrational number. B. if the area of a circle is a rational number, then the circumference of this circle is also a rational number. C. If the radius of a circle is an irrational number, the area is also an irrational number. D. If the circumference of a circle is a rational number, then the area of this circle is also a rational number.

## Step 1<br />The problem involves understanding the properties of circles and the nature of rational and irrational numbers.<br /><br />## Step 2<br />Let's analyze each option:<br /><br />### A. <br />The diameter of a circle is twice its radius. If the diameter is an irrational number, then the radius, being half of the diameter, is also an irrational number. This statement is always true.<br /><br />### B. <br />The area of a circle is given by \( \pi r^2 \), where \( r \) is the radius. If the radius is an irrational number, the area will be irrational. However, if the radius is rational, the area can be rational. For example, if the radius is 1 (rational), the area is \( \pi \) (irrational). But if the radius is \( \sqrt{2} \) (irrational), the area is \( 2\pi \) (irrational). So, this statement is not always true.<br /><br />### C. <br />The area of a circle is given by \( \pi r^2 \). If the radius is irrational, the area will also be irrational. This statement is always true.<br /><br />### D. <br />The circumference of a circle is given by \( 2\pi r \), where \( r \) is the radius. If the circumference is rational, the radius can be rational or irrational. For example, if the circumference is \( 2\pi \) (rational), the radius is 1 (rational). But if the circumference is \( 3\pi \) (rational), the radius is \( \frac{3}{2} \) (rational). So, this statement is not always true.<br /><br />## Step 3<br />Based on the above analysis, the statement that is true only for some cases is option B.