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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

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

Circles O, P, and Q are tangent (see Exercise 40) at points X, Y, and Z. being as specific as possible, explain what type of triangle Δ P Q O is if:

a) O X = 3 , P Y = 4 , Q Z = 1

b) O X = 2 , P Y = 2 , Q Z = 2 .

To determine

a)

To find:

To explain what type of triangle ΔPQO is if:

OX=3,PY=4,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,

OP

To determine

b)

To find:

To explain what type of triangle ΔPQO is if:

OX=2,PY=2,QZ=2

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