   Chapter 6.CT, Problem 9CT 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 ⊙ O with diameter A C ¯   , O C = 5 and A B = 6   . If M is the midpoint of B C ¯ , find A M . To determine

To find:

AM of the circle O

Explanation

Given:

O with diameter AC¯, OC=5 and AB=6.

M is the midpoint of BC¯.

Theorem used:

An angle inscribed in a semicircle is a right angle”.

Calculation:

Consider,

Here OC is the radius of the circle given by OC=5.

Thus it is clear that the diameter AC=2(OC)=2(5)=10.

From the theorem it is clear that “an angle inscribed in a semicircle is a right angle”.

Here AC¯ formed a semicircle by B intercepts with the diameter.

Thus, ΔABC from a right angle.

Using Pythagoras theorem,

AC2=AB2+BC2102=62+BC210262=BC210036=BC264=BC2BC=8

Thus the length of BC is 8

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