Question

Which of the following pairs of lines in a circle cannot be parallel:

• A. Two diameters of a circle
• B. Two chords of a circle
• C. A chord and a tangent of a circle
• D. Two tangents of a circle

Hint:

In a circle, a chord and a tangent at the same point are always perpendicular and cannot be parallel.

Answer 1

The Correct Option is C

To understand which of the pairs cannot be parallel, let's examine each case: Step 1: Two diameters of a circle.
Two diameters of a circle are always perpendicular to each other, so they cannot be parallel.
Step 2: Two chords of a circle.
Two chords of a circle can be parallel depending on the position of the chords.
Step 3: A chord and a tangent of a circle.
A chord and a tangent can never be parallel because the tangent touches the circle at only one point and is always perpendicular to the radius at that point.
Step 4: Two tangents of a circle.
Two tangents to a circle at any given point of contact with the circle can be parallel, as they can be at equal distances from the center.

Step 5: Conclusion.
Therefore, the correct answer is (iii) A chord and a tangent of a circle, as these can never be parallel. Final Answer:} A chord and a tangent of a circle.