Lesson Plan: Properties of Tangents and Chords Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the equation of a tangent to a circle and the equation of a perpendicular bisector of a chord using their perpendicularity.
Objectives
Students will be able to
- understand that tangents to circles are perpendicular to the radius at the point of intersection,
- understand that perpendicular bisectors to a chord of a circle pass through the center of the circle,
- find the equation of the tangent to a circle at a given point,
- find two possible tangents to a circle given the gradient of the tangent,
- find the center of a circle given one of its coordinates and the endpoints of a chord by finding the perpendicular bisector of the chord.
Prerequisites
Students should already be familiar with
- equations of circles,
- equations of perpendicular lines,
- finding the perpendicular bisector of a line segment,
- finding the intersection points of circles and lines.
Exclusions
Students will not cover
- finding the intersection of two perpendicular bisectors,
- circumcircles.
