Investigation: Construct a tangent to a circle from a point

Recall that a tangent segment is a segment that intersects the circumference of a circle in exactly one point, the point of tangency.

Use the video below and the lessons on basic constructions to construct the tangents to a circle from a given point.

Extra Challenges:

1.  Use your construction to verify the theorem, "If two tangents are drawn from a common point, the tangents are equal."

2.  Use your construction and the Pythagorean theorem to verify that "A tangent segment is perpendicular to the radius at the point of tangency."

3.  Draw two circles.  Construct all segments tangent to both circles from a single point.