If radii of two concentric circles are `4` `cm` and `5` `cm`, then length of each chord of one circle which is tangent to the other circle, is

Options

A. 3 cm
B. 6 cm
C. 9 cm
D. 1 cm

Explanation

To find the length of each chord of the larger circle that is tangent to the smaller circle, we can follow these steps:

### Step 1: Understand the Problem
We have two concentric circles with a common center O. The radius of the smaller circle (C1) is 4 cm, and the radius of the larger circle (C2) is 5 cm. We need to find the length of a chord of the larger circle that is tangent to the smaller circle.

### Step 2: Draw the Diagram
Draw two concentric circles with center O. Label the radius of the smaller circle (C1) as 4 cm and the radius of the larger circle (C2) as 5 cm. Mark a point A on the larger circle and draw a chord AB such that it is tangent to the smaller circle at point B.

### Step 3: Identify the Right Triangle
Since the chord AB is tangent to the smaller circle at point B, we can draw a perpendicular line from O to the chord AB. Let this point where the perpendicular meets the chord be point C. In triangle OBC, we have:
- OB = 4 cm (radius of the smaller circle)
- OC = 5 cm (radius of the larger circle)

### Step 4: Apply the Pythagorean Theorem
Triangle OBC is a right triangle (since OC is perpendicular to AB). We can use the Pythagorean theorem to find the length of BC.

Using the Pythagorean theorem:
\[ OC^2 = OB^2 + BC^2 \]
Substituting the values:
\[ 5^2 = 4^2 + BC^2 \]
\[ 25 = 16 + BC^2 \]
\[ BC^2 = 25 - 16 \]
\[ BC^2 = 9 \]
\[ BC = 3 \, \text{cm} \]

### Step 5: Calculate the Length of the Chord
Since the chord AB is bisected by the perpendicular OC, we have:
\[ AB = 2 \times BC \]
\[ AB = 2 \times 3 \]
\[ AB = 6 \, \text{cm} \]

### Conclusion
The length of each chord of the larger circle that is tangent to the smaller circle is **6 cm**.

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