Answer:
Radius, r, is 3.75
Step-by-step explanation:
From the given diagram,
AB = 9
AC = 6 + r
BC = r
Thus applying the Pythagoras theorem, we have;
[tex]/AC/^{2}[/tex] = [tex]/AB/^{2}[/tex] + [tex]/BC/^{2}[/tex]
[tex](6 + r)^{2}[/tex] = [tex]9^{2}[/tex] + [tex]r^{2}[/tex]
36 + 12r + [tex]r^{2}[/tex] = 81 + [tex]r^{2}[/tex]
collecting like terms,
12r = 81 - 36
12r = 45
r = [tex]\frac{25}{12}[/tex]
= 3.75
r = 3.75
The radius is 3.75.
