Question

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

Answer 1

Radius, r, is 3.75

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 =
`(25)/(12)`

= 3.75

r = 3.75

The radius is 3.75.