Question

Lines \( l \) and \( m \) are parallel. \( O \) is the center of the circle. The measure of angle \( d \) is \( 45^\circ \). The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \). Line \( RS \) forms a right angle with line \( m \). What is the diameter of circle O?

• A. 1
• B. \( \sqrt{2} \)
• C. \( 1\sqrt{2} \)
• D. \( \sqrt{2}/2 \)

Hint:

When dealing with right triangles and circles, always remember the relationship between the radius and diameter, and use trigonometry when applicable.

Answer 1

The Correct Option is B

Step 1: Analyze the figure.
We know that line \( RS \) is a radius of the circle, and it forms a right angle with line \( m \). Using the properties of a right triangle and the given length of line \( RS \), we can deduce that the diameter is \( \sqrt{2} \).
Step 2: Conclusion.
The diameter of the circle is \( \sqrt{2} \).