   Chapter 6.2, Problem 24E 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

In Exercises 23 to 25 , complete a paragraph proof. Given: Diameter A B ¯ ⊥ C E ¯ at D Prove: C D is the geometric mean of A D and D B To determine

To find:

The prove,. CD is the geometric mean of AD and DB.

Explanation

Calculation:

Given, diameter AB¯CE¯ at D in the given figure.

To prove: CD is the geometric mean of AD and DB.

i.e, to prove, CD2=ADDB.

From the figure, AB¯ is the diameter and AB¯CE¯.

The diameter on a chord bisects it.

CD=DE

E and B are angles with vertex on the circle.

Thus,

mB=mAC2mE=mAC2

From the above, mB=mE

Then,

The vertical angles are equal

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