Question

Point B is a point of tangency. Find the radius r of OC. А 9 B r n

Answer 1

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;

$/AC/^{2}$ = $/AB/^{2}$ + $/BC/^{2}$

$(6 + r)^{2}$ = $9^{2}$ + $r^{2}$

36 + 12r + $r^{2}$ = 81 + $r^{2}$

collecting like terms,

12r = 81 - 36

12r = 45

r = $\frac{25}{12}$

   = 3.75

r = 3.75

The radius is 3.75.