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.
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:
Wrap Up and Homework:
Answer the following questions in your math journals: How do you know that PQ is tangent to circle O? Why does this tangent construction work?
Activities for Tomorrow:
Use The Geometer's Sketchpad to consruct the tangent to a circle through an external point.