Question

In the diagram shown to the right, GH and KM are perpendicular bisectors of the chords they intersect. What can youconclude about the center of the circle? Justify your answer.

Answer 1

In circle geometry, there is a theorem which states that;

The perpendicular bisector of a chord passes through the center of a circle.

GH and KM are the perpendicular bisectors of both chords. They therefore pass through the center of the circle. Also, since they pass through the center of the circle, they are both diameters of the circle. Their point of intersection or where both (GH and KM) meet is the center of the circle.

Looking at the above explanation, the option which satisfies this explanation is option D.

Therefore, option D is the correct answer.