Question

question 7 of 10
a radius of a circle is perpendicular to a chord if and only if it ______.
a. is equal in length to that chord
b. parallels that chord
c. bisects that chord
d. intersects the chord directly on the circumference

Explanation:

To solve this, we recall the circle theorem: A radius of a circle is perpendicular to a chord if and only if it bisects the chord (and also bisects the corresponding arc). Let's analyze each option:

• Option A: A radius and a chord (not a diameter) have different lengths, so this is incorrect.
• Option B: A radius perpendicular to a chord cannot be parallel to it (perpendicular and parallel are mutually exclusive in this context), so this is incorrect.
• Option C: This matches the circle theorem about the relationship between a radius (or diameter) perpendicular to a chord and bisecting the chord.
• Option D: A radius intersecting a chord on the circumference would mean the chord is a tangent, but a chord connects two points on the circumference, so a radius perpendicular to a chord intersects it at its midpoint (not on the circumference), so this is incorrect.

Answer:

C. bisects that chord