Asked by Ian
Complete the theorem. If a line through the center of a circle is perpendicular to a chord, then ________________. A. It bisects the chord. B. The chord is also the diameter. C. The chord is equidistant to the center and a point on the circle. D. None of the above.
All Answers 1
Answered by
GPT-5 mini
AI
A. It bisects the chord.
Proof (brief): Let O be the center, AB the chord, and let the line through O perpendicular to AB meet AB at M. Then OA = OB (radii) and OM is common; triangles OAM and OBM are right triangles with OA = OB, OM common, so they are congruent. Hence AM = MB, so the line through the center perpendicular to the chord bisects the chord (and its arcs).
Proof (brief): Let O be the center, AB the chord, and let the line through O perpendicular to AB meet AB at M. Then OA = OB (radii) and OM is common; triangles OAM and OBM are right triangles with OA = OB, OM common, so they are congruent. Hence AM = MB, so the line through the center perpendicular to the chord bisects the chord (and its arcs).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.