2 concentric circles are of radii 5 cm and 3 cm.f

To find the length of the chord of the larger circle that touches the smaller circle, we can use some geometry concepts. Here’s how to approach the problem:

Understanding the Setup

We have two concentric circles:

• The larger circle has a radius of 5 cm.
• The smaller circle has a radius of 3 cm.

Visualizing the Chord

The chord of the larger circle that touches the smaller circle is perpendicular to the radius of the larger circle at the point of tangency. This means we can form a right triangle.

Applying the Pythagorean Theorem

In this right triangle:

• The distance from the center of the circles to the point where the chord touches the smaller circle is 3 cm (the radius of the smaller circle).
• The distance from the center to the chord (the radius of the larger circle) is 5 cm.
• The half-length of the chord is the other side of the triangle.

Calculating the Length

Let’s denote:

• r1 = 5 cm (radius of the larger circle)
• r2 = 3 cm (radius of the smaller circle)
• h = distance from the center to the chord = r1 - r2 = 5 cm - 3 cm = 2 cm

Using the Pythagorean theorem:

Let x be half the length of the chord. Then:

x² + h² = r1²

x² + 2² = 5²

x² + 4 = 25

x² = 21

x = √21 cm

Finding the Full Length of the Chord

The full length of the chord is twice the half-length:

Length of the chord = 2x = 2√21 cm.

Final Answer

The length of the chord of the larger circle that touches the smaller circle is approximately 9.16 cm.