we know that perpendicular from center bisects the chordby Pythagoras thm ,100+36=(1/2 of chord)^2√136=1/2 of chord2√34=1/2 of chord chord =2√34cm

The Problem:
We are given a circle with a radius of 10 cm and a chord that is 6 cm away from the center of the circle. We need to find the length of this chord.

Solution:
To find the length of the chord, we can use the Pythagorean theorem and some basic geometry concepts.

Step 1: Understanding the Problem:
Let's first understand the given information and the problem at hand.

- We have a circle with a radius of 10 cm.
- There is a chord in the circle that is 6 cm away from the center of the circle.
- We need to find the length of this chord.

Step 2: Drawing the Diagram:
To visualize the problem better, let's draw a diagram of the circle and the chord.

- Draw a circle of radius 10 cm.
- Mark the center of the circle and label it as point O.
- Draw a line segment from the center to a point on the circumference of the circle and label it as OB, where B is a point on the circumference.
- Draw another line segment parallel to OB at a distance of 6 cm and label it as CD, where C and D are points on the circumference.

Step 3: Applying Geometry Concepts:
Now, let's use some geometry concepts to find the length of the chord.

- In a circle, any line passing through the center and terminating at the circumference is called a radius.
- The line segment OB is a radius of the circle, and its length is 10 cm.
- The line segment CD is parallel to OB and is 6 cm away from it.
- Since OB is a radius, OC and OD are also radii of the circle with a length of 10 cm.
- OBCD is a rectangle, and its diagonals are equal in length.

Step 4: Finding the Length of the Chord:
To find the length of the chord, we need to find the length of the diagonal of the rectangle OBCD.

- Since OBCD is a rectangle, OC and OD are equal in length, and both are radii of the circle with a length of 10 cm.
- The length of OC and OD is 10 cm each.
- The diagonal of a rectangle can be found using the Pythagorean theorem.
- Applying the Pythagorean theorem, we have:
- OB² = OC² + BC²
- OB² = 10² + 6²
- OB² = 100 + 36
- OB² = 136

- Taking the square root of both sides, we get:
- OB = √136
- OB ≈ 11.66 cm

Therefore, the length of the chord is approximately 11.66 cm.