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 length of line PR?

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

Hint:

In right triangles, the length of the hypotenuse is often related to the legs by the Pythagorean theorem or trigonometric ratios like sine, cosine, and tangent.

Answer 1

The Correct Option is C

Step 1: Analyze the given information.
We are given that lines \( l \) and \( m \) are parallel, \( O \) is the center of the circle, and the measure of angle \( d \) is 45°. The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \) and line \( RS \) forms a right angle with line \( m \).
Step 2: Conclusion.
Using basic trigonometric relationships in the right triangle, we can deduce that the length of line \( PR \) is \( \sqrt{2} \).