Question

In a circle, if a diameter bisects a chord (that is not a diameter), then:

Answer 1

The chord and the diameter are perpendicular.

Suppose that chord AB is bisected by a diameter, which interserct the chord at point C.

Now, focus on triangles OAC and OBC. They have:

• OA = OB because they are both radii
• OC in common
• AC=BC because the diameter bisects the chord

So, they are congruent. In particular, this means that angles ACO and BCO are equal. Since they sum up to 180, each of them must be 90°, so the diameter is perpendicular to the chord.