McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 9.4, Problem 5ST1
Solution

To find: length of the chord

  410

Given:

Chord is 3 cm from the center of the circle of radius 7 cm.

Concept Used:

Theorem 8-2 The Square of the hypotenuse of right triangle is equal to the sum of the squares of the sides in a right triangle.

Explanation:

Consider the figure representing the given question:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 9.4, Problem 5ST1

Let PR¯ be the required chord and let OQ¯ be perpendicular to the chord PR¯ .

Then, by theorem 9-5, it can be said that OQ¯ bisects PR¯ .

That is,

  PQ=QR

Let QR=x

Consider the right triangle OQR .

Now, OR¯ is the hypotenuse and has length 7 and the lengths of the legs are QR=x and OQ=3 .

So, by theorem 8-2,

  OR2=OQ2+QR272=32+x249=9+x2

  499=x240=x2

Now, take square root of both sides,

  x2=40x=210

So, QR=210

Then,

PR=PQ+QR=QR+QR=210+210=410 [ PQ=QR ]

So, the length of the chord is 410 .

Chapter 9 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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Prob. 24WECh. 9.7 - Prob. 25WECh. 9.7 - Prob. 26WECh. 9.7 - Prob. 27WECh. 9.7 - Prob. 28WECh. 9.7 - Prob. 1ST2Ch. 9.7 - Prob. 2ST2Ch. 9.7 - Prob. 3ST2Ch. 9.7 - Prob. 4ST2Ch. 9.7 - Prob. 5ST2Ch. 9.7 - Prob. 6ST2Ch. 9.7 - Prob. 7ST2Ch. 9.7 - Prob. 8ST2Ch. 9.7 - Prob. 1ECh. 9.7 - Prob. 2ECh. 9.7 - Prob. 3ECh. 9.7 - Prob. 4ECh. 9.7 - Prob. 5ECh. 9 - Prob. 1CRCh. 9 - Prob. 2CRCh. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - Prob. 6CRCh. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - Prob. 9CRCh. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - Prob. 13CRCh. 9 - Prob. 14CRCh. 9 - Prob. 15CRCh. 9 - Prob. 16CRCh. 9 - Prob. 17CRCh. 9 - Prob. 18CRCh. 9 - Prob. 19CRCh. 9 - Prob. 20CRCh. 9 - Prob. 21CRCh. 9 - Prob. 22CRCh. 9 - Prob. 23CRCh. 9 - Prob. 24CRCh. 9 - Prob. 1CTCh. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Prob. 13CTCh. 9 - Prob. 14CTCh. 9 - 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