Question

At point A, Billy uses a compass to draw a circle, At point B, he draws another circle with the same radius he used for the first circle. The two circles intersect at point C and point D. Which of the following is always true ?

A.Segment CD is the perpendicular bisector of segment AB.
B.Segment CD is greater than Segment AB.
C.Segment CD is te diameter of the circles.
D.Segment AB is twice the length of Segment CD.

Answer 1

The answer is A. because CD bisects the circles.

Answer 2

A. Segment CD is the perpendicular bisector of segment AB.

Explanation:

Notice that the given circles intersect at two points. When that happens, it creates a symmetrcal area where the segment uniting the intersection points is perpendicular to the diameters. In this case that segment is CD.

Additionally, the resulting segment also divides equally the segment AB, because the intersection area is symmetrical.

Therefore, the right answer is A., because a perpendicular bisector intersects with a right angle and at the middle point, like CD does in this case.

(In the image attached you can observe the process)