Question

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Hint:

The radius drawn to the point of contact of a tangent always bisects the chord in this specific geometric configuration.

Answer 1

Given:
Two concentric circles (same centre) with radii:
Larger circle radius = 5 cm
Smaller circle radius = 4 cm

Step 1: Understanding the situation
A chord of the larger circle touches (is tangent to) the smaller circle.
The perpendicular distance from the centre to this chord = radius of smaller circle = 4 cm.

Step 2: Use the formula for chord length
For a circle of radius R, chord length at distance d from centre is:
Chord length = 2√(R² – d²)

Here, R = 5 cm and d = 4 cm.

Step 3: Substitute the values
Chord length = 2√(5² – 4²)
= 2√(25 – 16)
= 2√9
= 2 × 3
= 6 cm

Final Answer:
The length of the chord is 6 cm.