   Chapter 6.3, Problem 43E 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

Circles O, P, and Q are tangent (as shown for Exercise 40).If O X = 3 , P Y = 4 , Q Z = 1 , name:a) .The smallest angle of Δ P Q O b) .The smallest angle of Δ P Q O To determine

a)

To find:

To name the smallest angle of ΔPQO if:

OX=2,PY=3,QZ=1

Explanation

Given that, circles O, P, and Q are tangent (as shown) at points X, Y, and Z.

Then the value of OX=3,PY=4,QZ=1.

The diagrammatic representation is given below,

To find the measures of the sides of the triangle ΔPQO is given below,

OP=OX+PXPQ=PY+QYOQ=QZ+OZ

We know that OX=OZ,PX=PY,QY=QZ since radius of the circle is same for all points on the circle.

Substitute the value of OX=3,PY=4,QZ=1 and OX=OZ,PX=PY,QY=QZ to get the following,

O<

To determine

b)

To find:

To name the largest angle of ΔPQO if:

OX=2,PY=3,QZ=1

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