In the given figure, `AB` is a chord of a circle with centre `O` and `BOC` is a diameter . If `OD` `_|_` `AB` such that `OD` = `6` cm then `AC = ?`

Options

A. `9 cm`
B. `12 cm`
C. `15 cm`
D. `7.5cm`

Answer

B

Explanation

`OD _|_ AB implies` `D` is the midpoint of `AB`.
Also, `O` is the midpoint of `BC`.
Now, in `Delta BAC`, `D` is the midpoint of `AB` and `O` is the midpoint of `BC.`
`:. OD = (1)/(2) AC implies AC = 2 xxOD = (2 xx 6 ) cm = 12 cm`