Problem: The radius of a circle is 13 cm and the length of one of its chords is 10 cm. Find the distance of the chord from the center.

Solution:

To find the distance of the chord from the center of the circle, we can use the following steps:

Step 1: Identify the given information
- Radius of the circle: 13 cm
- Length of the chord: 10 cm

Step 2: Understand the properties of a circle
In a circle, the following properties hold true:
- The perpendicular bisector of a chord passes through the center of the circle.
- A radius that is perpendicular to a chord bisects the chord into two equal parts.

Step 3: Draw a diagram
Before we proceed with the calculations, let's draw a diagram to visualize the given information.


In the diagram, we have a circle with a radius of 13 cm. The chord has a length of 10 cm, and we need to find the distance of the chord from the center of the circle.

Step 4: Find the distance of the chord from the center
To find the distance of the chord from the center, we will use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we have a right-angled triangle with the following sides:
- Hypotenuse: Radius of the circle = 13 cm
- One side: Half the length of the chord = 10 cm / 2 = 5 cm (since the radius perpendicular to the chord bisects it)

Using the Pythagorean theorem, we can calculate the distance of the chord from the center:

Distance^2 = Radius^2 - Half chord length^2

Distance^2 = 13^2 - 5^2

Distance^2 = 169 - 25

Distance^2 = 144

Distance = √144

Distance = 12 cm

Therefore, the distance of the chord from the center of the circle is 12 cm.