Lesson Plan: Common Chords to Two Circles
This lesson plan includes the objectives and prerequisites of the lesson teaching students how to use the properties of the common chord between two intersecting circles to solve problems.
Objectives
Students will be able to
- use the fact that a common chord between two circles is a subset of the radical axis/power line of the two circles to find lengths of line segments,
- use the fact that the line segment connecting two circles’ centers bisects a common chord, along with circle theorems and the Pythagorean theorem, to find missing lengths,
- use the fact that the line segment connecting two circles’ centers intersects a common chord in a right angle to find missing angles,
- calculate the radii of circles, given the distance between their centers and the length of a common chord,
- calculate the length of a common chord, given the distance between the circles’ centers and their radii/areas/circumferences,
- use the fact that the line segment connecting two circles’ centers bisects the angle subtended by the minor arc between their points of intersection to find missing angles.
Prerequisites
Students should already be familiar with
- circle theorems,
- the Pythagorean theorem,
- the similarity of triangles,
- theorems about the power of a point.
