In two concentric circles centered at $O$, a chord $AB$ of the larger circle touches the smaller circle at $C$. If $OA = 3.5$ cm, $OC = 2.1$ cm, then $AB$ is equal to
In two concentric circles centered at $O$, a chord $AB$ of the larger circle touches the smaller circle at $C$. If $OA = 3.5$ cm, $OC = 2.1$ cm, then $AB$ is equal to
We are given two concentric circles centered at $O$, where the chord $AB$ of the larger circle touches the smaller circle at $C$. Given:
$OA = 3.5$ cm,
$OC = 2.1$ cm.
We need to find the length of $AB$.
### Step 1: Identify Right Triangle
Since $AB$ is a chord of the larger circle and touches the smaller circle at $C$, the radius $OC$ is perpendicular to $AB$ at $C$. This means that $OC$ bisects $AB$, so:
$AC = CB = \frac{AB}{2}$.
In the right triangle $OAC$, using the Pythagorean theorem: