Question

Consider the following procedure.

1. From a point A outside a circle, draw a line to the circle's center, C.
2. Construct the perpendicular bisector of AC, and label the midpoint of 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 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° O
D. Concentric circles centered at point X​

Answer 1

Answer: A. A tangent to the circle

Explanation: By following the procedure, we are constructing a tangent line to the given circle, which is a line that touches the circle at only one point, in this case at the point of intersection X. A tangent line is at right angles (90°) to the radius of the circle and is perpendicular to the line joining the center of the circle to the point at which the tangent touches the circle.

Starting from the given point A outside the circle, we first draw a line to the circle's center C. Next, we construct the perpendicular bisector of AC to find its midpoint E. After that, we place the compass point at point E and set the width to EA. Then, we draw an arc that intersects the circle, and label the point of intersection as point X. Lastly, we draw the line AX, which is the line that we have constructed.

Therefore, the answer is A. A tangent to the circle.