A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away

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Question: A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away from the center?

Options:

Correct Answer: 12

Solution:

Using the formula: chord length = 2√(radius² - distance from center²). Here, chord length = 2√(10² - 8²) = 2√(100 - 64) = 2√36 = 12.

A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away from the center?

A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away from the center?

Step 1: Identify the radius of the circle, which is given as 10 cm.
Step 2: Identify the distance from the center to the chord, which is given as 8 cm.
Step 3: Use the formula for chord length: chord length = 2√(radius² - distance from center²).
Step 4: Substitute the values into the formula: chord length = 2√(10² - 8²).
Step 5: Calculate 10², which is 100.
Step 6: Calculate 8², which is 64.
Step 7: Subtract 64 from 100: 100 - 64 = 36.
Step 8: Take the square root of 36, which is 6.
Step 9: Multiply by 2: 2 * 6 = 12.
Step 10: The length of the chord is 12 cm.

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