Question

consider the following procedure.

1. from a point a outside a circle, draw a line to the circles center, c.
2. construct the perpendicular bisector of $overline{ac}$, and label the midpoint of $overline{ac}$ as point e.
3. place the compass point at point e, and set the width to ea.
4. draw an arc that intersects the circle, and label the point of intersection as point x.
5. draw $overline{ax}$.

what has been constructed by the above procedure?
a. a tangent to the circle
b. a perpendicular bisector of the diameter
c. an inscribed angle with a measurement of 90°
d. concentric circles centered at point x

Explanation:

When we follow the given construction steps, we are creating a line from an external point A to a point X on the circle. The key geometric property here is that the angle formed between the radius (CX) and the line AX is 90 degrees. This is a characteristic property of a tangent - a line that touches a circle at exactly one point and is perpendicular to the radius at that point.

Answer:

A. A tangent to the circle