In a circle, if the radius is 8 cm and a chord is 12 cm long, what is the distan

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Question: In a circle, if the radius is 8 cm and a chord is 12 cm long, what is the distance from the center of the circle to the chord?

Options:

Correct Answer: 6

Solution:

Using the formula d = √(r² - (c/2)²): d = √(8² - (12/2)²) = √(64 - 36) = √28 ≈ 5.29.

In a circle, if the radius is 8 cm and a chord is 12 cm long, what is the distance from the center of the circle to the chord?

In a circle, if the radius is 8 cm and a chord is 12 cm long, what is the distance from the center of the circle to the chord?

Step 1: Identify the radius of the circle, which is given as 8 cm.
Step 2: Identify the length of the chord, which is given as 12 cm.
Step 3: Calculate half the length of the chord. Since the chord is 12 cm long, half of it is 12/2 = 6 cm.
Step 4: Use the formula d = √(r² - (c/2)²) to find the distance from the center of the circle to the chord.
Step 5: Substitute the values into the formula: d = √(8² - 6²).
Step 6: Calculate 8², which is 64.
Step 7: Calculate 6², which is 36.
Step 8: Subtract 36 from 64: 64 - 36 = 28.
Step 9: Take the square root of 28: √28.
Step 10: Simplify √28 to approximately 5.29 cm.

Circle Geometry – Understanding the relationship between the radius, chord length, and distance from the center to the chord.
Pythagorean Theorem – Applying the Pythagorean theorem to find distances in a right triangle formed by the radius, half the chord, and the distance from the center to the chord.