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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given: Concentric circles with center Q
S R = 3  and  R Q = 4
Q S ¯ T V ¯  at  R
Find: a) R V
b) T V

Exercises 16, 17

To determine

a)

To find: RV¯.

Explanation

Given:

Concentric circles with centre Q with SR=3,RQ=4 and QS¯ is perpendicular to TV¯ at R.

Definition:

Segment addition postulate:

If X is a point on AB¯ and A-X-B, then AX¯+XB¯=AB¯.

Calculation:

Given that QS¯ is perpendicular to TV¯.

Therefore QRV=90.

Hence ΔQRV is a right triangle.

By segment addition postulate, QS¯=SR¯+RQ¯.

We have SR=3,RQ=4

QS¯=SR¯+RQ¯=3+4QS¯=7

From the figure, we see that QS and QV are radii of the outer circle

To determine

b)

To find: TV¯.

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