If a circle has a radius of 5 units, what is the length of a chord that is 4 uni

₹0.0

Question: If a circle has a radius of 5 units, what is the length of a chord that is 4 units away from the center?

Options:

Correct Answer: 8

Solution:

Using the formula: chord length = 2 * √(radius² - distance from center²) = 2 * √(5² - 4²) = 2 * √(25 - 16) = 2 * √9 = 6.

If a circle has a radius of 5 units, what is the length of a chord that is 4 units away from the center?

If a circle has a radius of 5 units, what is the length of a chord that is 4 units away from the center?

Step 1: Identify the radius of the circle, which is given as 5 units.
Step 2: Identify the distance from the center to the chord, which is given as 4 units.
Step 3: Use the formula for the length of a chord: chord length = 2 * √(radius² - distance from center²).
Step 4: Substitute the radius and distance into the formula: chord length = 2 * √(5² - 4²).
Step 5: Calculate 5², which is 25.
Step 6: Calculate 4², which is 16.
Step 7: Subtract 16 from 25: 25 - 16 = 9.
Step 8: Take the square root of 9, which is 3.
Step 9: Multiply by 2: 2 * 3 = 6.
Step 10: The length of the chord is 6 units.

Circle Geometry – Understanding the properties of circles, including radius, chords, and distances from the center.
Pythagorean Theorem – Applying the Pythagorean theorem to find relationships between the radius, distance from the center, and chord length.