Question

question 1 of 10

true or false? if a radius of a circle intersects a chord, then it bisects that chord.

a. true
b. false

Explanation:

Analyze the geometric condition for chord bisection

A radius only bisects a chord if it is perpendicular to that chord (excluding the diameter case). If a radius merely intersects a chord at an oblique angle, it does not bisect it.

Construct a counterexample

Consider a circle with a chord that is not a diameter. Draw a radius that intersects this chord at any point other than its midpoint (i.e., not perpendicularly). The chord is divided into two unequal segments, so it is not bisected.

Determine the truth value

Since the statement "If a radius of a circle intersects a chord, then it bisects that chord" does not hold for all cases, the statement is false.

Answer:

• (A) True
• (B) False (Correct answer)