The radius of the circle is 34 and the chord is 44. How far is the chord from the center?


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

### Step 1: Identify the given values.
- Radius \( r = 34 \) units
- Chord length \( AB = 44 \) units

### Step 2: Draw the circle and label the center as \( O \). Let the chord \( AB \) be the line segment. Drop a perpendicular from the center \( O \) to the chord \( AB \), and label the point of intersection as \( P \). \( OP \) is the distance from the center of the circle to the chord.

### Step 3: Apply the Pythagorean theorem.
Since \( OP \) is perpendicular to the chord \( AB \), it bisects \( AB \) into two equal segments. Therefore, \( AP = PB = \frac{44}{2} = 22 \) units.

Now, in the right triangle \( OPA \):
- \( OA = r = 34 \) units (radius)
- \( AP = 22 \) units (half of the chord)

Using the Pythagorean theorem:
\[
OP = \sqrt{OA^2 - AP^2}
\]
\[
OP = \sqrt{34^2 - 22^2}
\]
\[
OP = \sqrt{1156 - 484}
\]
\[
OP = \sqrt{672}
\]
\[
OP = \sqrt{144 \times 4.67} \approx \sqrt{144} \times 2 \times 1.082  = 12 \times 2 \times 1.082 \approx 25.92 \text{ units}
\]

### Conclusion:
The distance from the center of the circle to the chord is approximately **25.9 units**.

Would you like more details or have any questions?

Here are five related questions:
1. How do you find the length of a chord when given the radius and distance from the center?
2. What is the significance of the perpendicular from the center to a chord in a circle?
3. How do you find the radius of a circle when given the distance from the center to a chord and the chord length?
4. Can you find the area of a sector formed by the radius and the chord?
5. How does the Pythagorean theorem apply to circles in general?

**Tip:** When working with circles, always remember that a perpendicular from the center to a chord bisects the chord, creating two equal segments.

Discover how to calculate the distance from the center of a circle to a chord using the Pythagorean theorem. This problem involves a circle with a radius of 34 units and a chord length of 44 units. Suitable for students in Grades 9-12.

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