Question

As part of her school project, Maria had to construct tangent lines through a point outside a circle. She used the following steps to complete the task:

Step 1: Use a straightedge to connect the center of the circle with the external point.
Step 2: Bisect that line segment by using a ruler to find the midpoint.
Step 3: Create a new circle that will pass through both the external point and the center of the original circle.
Step 4: Create the tangent lines by connecting the external point to the points where the two circles intersect.

When she was finished, Maria realized that her construction was incorrect. Analyze her process and determine where the mistake was made.

Step 1

Step 2

Step 3

Step 4

Answer 1

The mistake is in Step 2. She needs to find the midpoint of the segment that connects the external point and the center of the circle through proper construction, not by using a ruler.