A circle of radius 2.5 cm has a chord of length 4.8cm.Find the distance of the chord from the center of the circle

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

1. Let \( r = 2.5 \, \text{cm} \) be the radius of the circle, and \( AB = 4.8 \, \text{cm} \) be the length of the chord.
2. Draw a perpendicular from the center \( O \) of the circle to the chord \( AB \), meeting the chord at point \( M \). This line will bisect the chord, so \( AM = MB = \frac{AB}{2} = \frac{4.8}{2} = 2.4 \, \text{cm} \).
3. In the right triangle \( OMA \), the hypotenuse \( OA = 2.5 \, \text{cm} \) (the radius), and one leg \( AM = 2.4 \, \text{cm} \).
4. We need to find the distance \( OM \) (the perpendicular distance from the center to the chord). Using the Pythagorean theorem in triangle \( OMA \):

\[
OA^2 = OM^2 + AM^2
\]

Substituting the known values:

\[
(2.5)^2 = OM^2 + (2.4)^2
\]

\[
6.25 = OM^2 + 5.76
\]

\[
OM^2 = 6.25 - 5.76
\]

\[
OM^2 = 0.49
\]

\[
OM = \sqrt{0.49} = 0.7 \, \text{cm}
\]

So, the distance of the chord from the center of the circle is \( 0.7 \, \text{cm} \).

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions:
1. How does the Pythagorean theorem apply to circles?
2. What is the relationship between chords and radii in a circle?
3. How would the distance change if the chord length increased?
4. Can you solve the same problem for a larger radius?
5. How would you calculate the area of the circle using the radius?

**Tip:** Always draw a diagram when working with geometry problems. It helps visualize the relationships between different parts of the figure.

A circle of radius 2.5 cm has a chord of length 4.8 cm. Find the distance of the chord from the center of the circle.

Learn how to find the distance from the center of a circle (radius 2.5 cm) to a chord (length 4.8 cm). Using the Pythagorean theorem, this problem breaks down key geometry concepts and chord properties. Suitable for Grades 8-10.

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