Problem Statement
Two concentric circles are of radii $5\text{ cm}$ and $3\text{ cm}$. Find the length of the chord of the larger circle which touches the smaller circle.
Verified Solution & Marking Scheme
Identify Geometric Relations
Let common center be $O$. Let $AB$ be chord of larger circle touching smaller circle at $P$.
Radius of smaller circle $OP = 3\text{ cm}$ is perpendicular to tangent $AB$ ($OP \perp AB$).
Radius of larger circle $OA = 5\text{ cm}$.
Apply Pythagoras Theorem in Right Triangle OPA
$AP^2 = OA^2 - OP^2 = 5^2 - 3^2 = 25 - 9 = 16 \implies AP = 4\text{ cm}$
Calculate Full Chord Length AB
The perpendicular from the center to a chord bisects the chord:
$AB = 2 \times AP = 2 \times 4 = 8\text{ cm}$