In a circle, if the radius is 10 units and a chord is 8 units long, what is the

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Question: In a circle, if the radius is 10 units and a chord is 8 units long, what is the distance from the center of the circle to the chord?

Options:

Correct Answer: 6

Solution:

Using the formula: distance = √(radius² - (chord length/2)²) = √(10² - (8/2)²) = √(100 - 16) = √84 ≈ 9.17.

In a circle, if the radius is 10 units and a chord is 8 units long, what is the distance from the center of the circle to the chord?

In a circle, if the radius is 10 units and a chord is 8 units 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 10 units.
Step 2: Identify the length of the chord, which is given as 8 units.
Step 3: Calculate half of the chord length. Since the chord is 8 units long, half of it is 8/2 = 4 units.
Step 4: Use the formula to find the distance from the center of the circle to the chord: distance = √(radius² - (chord length/2)²).
Step 5: Substitute the values into the formula: distance = √(10² - 4²).
Step 6: Calculate 10², which is 100.
Step 7: Calculate 4², which is 16.
Step 8: Subtract 16 from 100: 100 - 16 = 84.
Step 9: Take the square root of 84: distance = √84.
Step 10: Approximate √84, which is about 9.17 units.

Circle Geometry – Understanding the relationship between the radius, chord length, and the distance from the center to the chord.
Pythagorean Theorem – Applying the theorem to find the distance from the center of the circle to the chord using right triangle properties.