# Straight Edge and Compass Construction of the Tangent to a Circle Through an External Point

Objective:
Given a circle and an external point, the students will be able to construct a tangent to the circle through the point using a straightedge and compass. They will also be able to explain why this construction works.

Opening Activity:
Have a class discussion about what being tangent means. Also, review that a triangle inscribed in a circle on the diameter of the circle is always a right triangle.

Order of Activities:
Give the students five minutes to work on the construction on their own or in pairs. After five minutes, bring the class together and go through the construction together:

• Construct a circle with center O and any point P outside the circle.
• Use a straightedge to construct the segment OP.

• Find the midpoint of OP by constructing two circles. One circle should have center P and radius OP, and the other circle should have center O and radius OP. Now construct a line l through the intersection points of these two circles. This line will bisect OP. The intersection of line l and segment OP is the midpoint M of OP.