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If a chord is perpendicular to a segment drawn from the center of the circle, what do you know about the point where the segment and the chord intersect?

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Midpoint of the chord.
the point is the midpoint of a chord and will result in the segment being perpendicular to the chord

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Other answers:

Theorem: In a circle, a radius perpendicular to a chord bisects the chord. So, the point of interesection of the chord and the radius is the midpoint of the chord.
You don't need no theorem. Basically, you have an isosceles triangle, and its altitude (perpendicular line from the vertex) bistects the base, in this case the chord.

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