/*! 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. Quad. ABCD is circumscribed abou... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q14. (page 336)

Quad. ABCD is circumscribed about a circle. Discover and prove a relationship between AB+DC and AD+BC.

Short Answer

Expert verified

AB+DCand AD+BC

Step by step solution

01

Step 1. Given information.

Let ABCD be a quadrilateral circumscribing the circle with centre O. The quadrilateral touches the circle at point P,Q,R and S.

02

Step 2. Formula used.

Lengths of tangents drawn from external point are equal.

03

Step 3. Proof.

Consider the figure below,

According to theorem, lengths of tangents drawn from external point are equal.

Then,

AP=ASBP=BQCR=CQDR=DS

04

Step 4. Adding above equations.

AP+BP+CR+DR=AS+BQ+CQ+DSAP+BP+CR+DR=AS+SD+CQ+BQAB+CD鈥夆赌�=鈥�AD+BC

Hence, it is proved that, AB+CD=AD+BC

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 91影视!

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

For each exercise draw 鈯�O with radius 12. Then draw radii OA炉 and to OB炉 form an angle with the measure named. Find the length of AB炉.

d. m鈭�AOB=120掳

For each exercise draw 鈯�O with radius 12. Then draw radii OA炉and to OB炉 form an angle with the measure named. Find the length of AB炉.

b. m鈭�AOB=180掳

Find the measure of central 鈭�1.

Plane Z passes through the center of sphere Q.

  1. Explain why QR=QS=QT.
  2. Explain why the intersection of the plane and the sphere is a circle. (The intersection of a sphere with any plane passing through the center of the sphere is called a great circle of the sphere).

Name the diameter of 鈯�o.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.