Answer:
The radius is [tex]r=5\ cm[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<C =(1/2)[arc\ AB][/tex]
[tex]m<C =90\°[/tex]
substitute
[tex]90\°=(1/2)[arc\ AB][/tex]
[tex]arc\ AB=180\°[/tex]
That means----> The length side AB of the inscribed triangle is a diameter of the circle
Applying Pythagoras Theorem
Calculate the length side AB
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]
[tex]AB^{2}=8^{2}+6^{2}[/tex]
[tex]AB^{2}=100[/tex]
[tex]AB=10\ cm[/tex] -----> is the diameter
Find the radius
[tex]r=10/2=5\ cm[/tex] -----> the radius is half the diameter
