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10. CIRCLES

This chapter explores the properties and characteristics of tangents to circles, defining tangents as lines that touch the circle at a single point. It establishes that the tangent is perpendicular to the radius at the point of contact and examines the conditions under which tangents can be drawn from points both inside and outside the circle. Various activities and examples illustrate these concepts and highlight the equal lengths of tangents from an external point.

Sections

CIRCLES

This section explores the properties of circles, specifically focusing on the concept of tangents and their relationship to radius and secants.

10 Section Overview

Start current section content and materials

10.1 Introduction

This section introduces the concept of a circle and explores the relationship between a circle and lines, specifically focusing on tangents and secants.

10.2 Tangent to a Circle

This section defines tangents to circles, exploring their properties and existence.

10.3 Number of Tangents from a Point on a Circle

This section discusses how many tangents can be drawn from different positions relative to a circle: inside, on, or outside the circle.

10.4 Summary

This section outlines the main properties of tangents to a circle.

Learning Objectives

  • A circle consists of points at a constant distance (radius) from a center.

  • Tangents intersect a circle at only one point, while secants intersect at two.

  • The length of tangents drawn from an external point to a circle are equal.

  • The radius at the point of contact with the tangent is perpendicular to the tangent.

Key Concepts

Tangent

A line that intersects a circle at exactly one point.

Secant

A line that intersects a circle at two points.

Normal

The line containing the radius through the point of contact; it is perpendicular to the tangent.

Point of Contact

The point at which a tangent touches the circle.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting