THIS PROBLEM IS FROM THE CCSS

G-C.4. (+) Construct a tangent line from a point outside a given circle to the circle.

The problem says that I need to construct a tangent line from a point outside a circle to the circle.
What am I trying to solve? I am trying to figure out how to place this line so it is tangent.
The important/essential information is that I use the definition of a tangent line.

Hint: Review the Semicircle Theorem
Step 1. Given diagram with circle C and point A.

Step 2. Construct a circle (an arc is shown in the graphic) centered at point A through point C. Use the Tape Measure tool to draw a line connecting the intersection points. The intersection of segment AC and the dashed line indicates the midpoint of segment AC. This point is labeled M.

Step 3. Construct a circle centered at point M through point A (and C). Connect Point A to Point N. Recall that a triangle inscribed in a semicircle is a right triangle.

Caution: When I measure with the protractor tool, the angle is ~91.1 degrees. How can we improve the accuracy in this environment?

Summer 2017 - updated