A circle has a radius of 7 units. What is the length of a chord that is 4 units

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Question: A circle has a radius of 7 units. What is the length of a chord that is 4 units away from the center of the circle?

Options:

Correct Answer: 10

Solution:

Using the formula: chord length = 2 * √(radius² - distance from center²) = 2 * √(7² - 4²) = 2 * √(49 - 16) = 2 * √33 ≈ 11.55.

A circle has a radius of 7 units. What is the length of a chord that is 4 units away from the center of the circle?

A circle has a radius of 7 units. What is the length of a chord that is 4 units away from the center of the circle?

Step 1: Identify the radius of the circle, which is given as 7 units.
Step 2: Identify the distance from the center of the circle 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: Calculate the square of the radius: 7² = 49.
Step 5: Calculate the square of the distance from the center: 4² = 16.
Step 6: Subtract the square of the distance from the square of the radius: 49 - 16 = 33.
Step 7: Take the square root of the result: √33.
Step 8: Multiply the square root by 2 to find the chord length: 2 * √33.
Step 9: Calculate the approximate value of the chord length: 2 * √33 ≈ 11.55.

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