# Lesson Plan: Tangents of a Circle Mathematics • Third Year of Preparatory School

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the properties of tangents of circles to find missing angles or side lengths.

#### Objectives

Students will be able to

- recall the definition of a tangent to a circle,
- understand that a tangent and a radius which share a common point on the circumference of a circle are perpendicular to each other,
- understand that the lengths of tangent segments drawn from an external point to a circle are equal in length and understand corollaries derived from this theorem such as
- the bisector of the chord which connects to tangents,
- the bisector of the central angle and the angle whose vertex is at the external point,

- understand the definition of the inscribed circle of a polygon
- including how the center of the circle relates to the angle bisectors of the polygon,

- identify how to determine the center of the inscribed circle of a polygon,
- apply the properties of tangent of circles in order to find missing angles or side lengths, including systems
- with circles inscribed in polygons,
- with lines which are common tangents to more than one circle.

#### Prerequisites

Students should already be familiar with

- the Pythagorean theorem,
- properties of triangles,
- the central angle theorem,
- parallel chords and tangents,
- forming and solving linear equations,
- inscribed angle theorems,
- cyclic quadrilaterals,
- perpendicular bisector of a chord.

#### Exclusions

Students will not cover

- equation of a line (in any form),
- equation of a circle,
- angles of tangency.