Topicmb499df6c3b9fb7eb_1528449000663_0Topic

TangenttangentTangent to the circlecirclecircle

Levelmb499df6c3b9fb7eb_1528449084556_0Level

Second

Core curriculummb499df6c3b9fb7eb_1528449076687_0Core curriculum

IX. Analytic geometry on the Cartesian plane. Student:

6) finds common points of a straight line and a circle and a straight line and a parabola which is a graph of a quadratic function.

Timingmb499df6c3b9fb7eb_1528449068082_0Timing

45 minutes

General objectivemb499df6c3b9fb7eb_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmb499df6c3b9fb7eb_1528449552113_0Specific objectives

1. Constructing the tangenttangenttangent to the circle.

2. Applying properties of the tangent to the circlecirclecircle.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmb499df6c3b9fb7eb_1528450430307_0Learning outcomes

The student:

- constructs the tangent to the circlecirclecircle,

- applies properties of the tangenttangenttangent to the circle.

Methodsmb499df6c3b9fb7eb_1528449534267_0Methods

1. Brainstorming.

2. Discussion.

Forms of workmb499df6c3b9fb7eb_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmb499df6c3b9fb7eb_1528450127855_0Introduction

The teacher introduces the subject of the lesson – learning to construct the tangenttangenttangent to the circle.

Students revise most important properties of the tangent to the circlecirclecircle, using brainstorming.

Proceduremb499df6c3b9fb7eb_1528446435040_0Procedure

Task
Based on the picture, identify the angle between the radius of the circlecirclecircle going to the point of tangency and the tangent line. You also determine the distance from the centre of the circle to the tangenttangenttangent, depending on the length of the radius.

[Illustration 1]

Conclusion:

- If a line is tangent to the circle then the distance between the centre of the circle and the line is equal to the radius. 
- The radius that goes to the point of tangency is perpendicular to the tangent.mb499df6c3b9fb7eb_1527752263647_0- If a line is tangent to the circle then the distance between the centre of the circle and the line is equal to the radius. 
- The radius that goes to the point of tangency is perpendicular to the tangent.

Task
Students work individually, using computers. Their task is to observe ways of constructionconstructionconstruction of the tangenttangenttangent to the circlecirclecircle.

[Geogebra applet]  

Task
Draw any circle. Construct a tangent to the circle that goes through any point laying on the circumference.mb499df6c3b9fb7eb_1527752256679_0Draw any circle. Construct a tangent to the circle that goes through any point laying on the circumference.

Task
Draw any circle. Construct a tangenttangenttangent that goes through any point not laying on the circumferencepoint not laying on the circumferencepoint not laying on the circumference. How many tangents did you obtain?

What is the length of the line segments connecting a point that is not laying on the circumference and the points of tangency?

Lesson summarymb499df6c3b9fb7eb_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- If a line is tangent to the circle then the distance between the centre of the circle and the line is equal to the radius.
- The radius that goes to the point of tangency is perpendicular to the tangent.mb499df6c3b9fb7eb_1527752263647_0- If a line is tangent to the circle then the distance between the centre of the circle and the line is equal to the radius.
- The radius that goes to the point of tangency is perpendicular to the tangent.

Selected words and expressions used in the lesson plan

circlecirclecircle

constructionconstructionconstruction

description of the constructiondescription of the constructiondescription of the construction

line segment perpendicular to the lineline segment perpendicular to the lineline segment perpendicular to the line

point laying on the circumferencepoint laying on the circumferencepoint laying on the circumference

point not laying on the circumferencepoint not laying on the circumferencepoint not laying on the circumference

radius of a circleradius of a circleradius of a circle

tangenttangenttangent

tangent to a circletangent to a circletangent to a circle