Question

The radii of two concentric circles with centre \(O\) are \(10\) cm and \(6\) cm. If chord \(AB\) of the larger circle is tangent to the smaller circle, then the distance (in cm) of chord \(AB\) from centre \(O\) is

• A. 4
• B. 6
• C. 8
• D. 10

Hint:

For concentric circles:
• If a chord of the larger circle is tangent to the smaller circle, then \[ \boxed{\text{Perpendicular distance from the centre to the chord}=\text{Radius of the smaller circle}.} \]

Answer 1

The Correct Option is B

Concept: If a chord of a larger circle is tangent to a smaller concentric circle, then the perpendicular distance from the common centre to the chord is equal to the radius of the smaller circle.

Step 1: Use the property of tangency.
Since chord \(AB\) is tangent to the smaller circle, \[ \boxed{\text{Distance of }AB\text{ from }O=\text{Radius of the smaller circle}} \]

Step 2: Substitute the given value.
Radius of the smaller circle \[ =6\text{ cm}. \] Hence, \[ \boxed{\text{Distance of chord }AB\text{ from }O=6\text{ cm}.} \]

Step 3: Final conclusion.
Therefore, the required distance is \[ \boxed{6\text{ cm}.} \]