   Chapter 6.3, Problem 3E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Note: Exercises preceded by an asterisk are of a more challenging nature.Given: O V ¯ ⊥ R S ¯     i n     ⊙ O O V = 9     a n d     O T = 6 Find: R S To determine

To find:

To find RS.

Explanation

Given that OV¯RS¯ in O,OV=9 and OT=6

Consider the following figure,

Given that OV¯RS¯ in O then ΔORT is right triangle.

Pythagorean theorem:

In a right angled triangle then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Also OR=OV since radius are same for all points on a circle.

Consider the ΔORT to get the following,

OR2=OT2+TR2

Substitute the value of OV=OR=9 and OT=6 to get the following,

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