Question

In the given figure, AB is a chord of the circle with centre O and BOC is the diameter. If $OD\perp AB$ such that $OD=6\text{cm}$, then find AC.

• A. $12\text{cm}$
• B. $7.5\text{cm}$
• C. $15\text{cm}$
• D. $9\text{cm}$

Answer 1

The correct option is A $12\text{cm}$

$OD\perp AB....\left(i\right)$
$CA\perp AB....\left(ii\right)$
From (i) and (ii):
$OD||CA$
O is the midpoint of BC and OD || CA.
D is the midpoint of BA. .
(By the converse of the midpoint theorem.)
$OD=\frac{1}{2}\left(AC\right)$ (by the midpoint theorem)
$AC=2\left(OD\right)=2\ast 6=12\text{cm}$