/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q14. a. Given: WZ¯ is a diameter o... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 9: Q14. (page 342)

a. Given:WZ¯is a diameter of ⊙o;OX¯∥ZY¯

Prove: WXÁåœâ‰…XYÁåœ.

(Hint: draw OYÁåœ.)

Short Answer

Expert verified

(a)

The final answer is

Arc length WX≅arc length XY.

Step by step solution

01

Step 1. Given information:

WZ¯ is a diameter of circle and OX¯∥ZY¯

02

Step 2. Concept used:

We use basic geometric and angle concept

03

Step 3. Applying the concept:

First let us draw OY¯in the given figure.

Then OY¯and OZ¯becomes radii of the circles ⇒OY¯=OZ¯

Let ∠WOX=x°, since OX¯ ||ZY¯ then ∠OZY  =x°and also Δ OZYis isosceles triangles as OY¯=OZ¯then ∠OYZ  =x°

From Δ OZY, we have  ∠OZY+∠ZYO+∠YOZ=1800

⇒x∘+x∘+∠ZOY=180∘⇒∠ZOY=180∘−2x∘

Also from straight line WZ¯, we have  ∠WOX+∠XOY+∠ZOY=1800

⇒x∘+∠XOY+180∘−2x∘=180∘⇒∠XOY−x∘=180−180∴∠XOY=x∘

Thus, ∠WOX=x°=∠XOY

⇒Arcs made by same angle in a circle are congruent.

Hence, Arc length WX  ≅arc lengthXY.

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.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

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

JT¯is tangent to ⊙Oat T. Complete.

If m∠TOJ=60 and OT=6, then JO=?

RS¯ and TU¯are common internal tangents to the circles. If RZ=4·7 and ZU=7·3, Find RS and TU.

Use a compass to draw a large ⊙o.Draw a central ∠AOB..

a. draw three other points P,Qand R that are on ⊙obut not on ABÁåœ.

then draw ∠APB,∠AQB and ∠ARB.

b. Use a protractor to find m∠AOB,m∠APB,m∠AQB and m∠ARB.

c. What is the relationship between m∠APB,m∠AQB and m∠ARB?

What is the relationship between m∠AOBand m∠APB?

PA¯, PB¯,and RS¯ are tangents.

Explain, Why PR+RS+SP=PA+PB.

In Exercises 17-20, the latitude of a city is given. Sketch the earth and a circle of latitude through the city. Find the radius of this circle.

Rio de Jamarion; 23°S
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.