Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q22. (page 337)

Prove theorem 9.2

Short Answer

Expert verified

A tangent can touch a circle at only one point.

Step by step solution

01

Step 1. Statement.

A tangent can touch a circle at only one point.

02

Step 2. Draw the figure.

Consider a line in the plane of a circle perpendicular to a radius at its outer endpoint.

In the below figure line lis the plane of circle with center Qand l⊥QR.

03

Step 3. Concept used.

Suppose lis not tangent to circle then lis touching the circle at some other point P, then QP=QR.

This is because both are radius, and they both make same angle.

Since, l⊥QR then l⊥QP also but ΔQPRcannot have two 90°angle.

Therefore, lcannot touch the circle at two points, so line ltouch the circle at only R.

Therefore, by definition of tangent line lis tangent to circle.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In exercises 2-7find the measure of the arc.

BAD⏜

Name the diameter of ⊙o.

JT¯is tangent to ⊙Oat T. Complete.

If m∠TOJ=60 and OT=6, then JO=?

The number of odd vertices will tell you whether or not a network can be traced without backtracking. Do you see how? If not, read on.

Tell why it is impossible to walk across the seven bridges of Koenigsberg without crossing any bridge more than once.

Draw ⊙Owith perpendicular radii OX¯and OY¯. Draw tangents to the circle at X and Y.

a. If the tangents meet at Z, what kind of figure is OXYZ? Explain.

b. If OX=5, find OZ.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free