If a chord of a circle is 16 units long and the radius is 10 units, what is the

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Question: If a chord of a circle is 16 units long and the radius is 10 units, what is the distance from the center of the circle to the chord?

Options:

Correct Answer: 8

Solution:

Using the formula: distance = √(radius² - (half of chord length)²) = √(10² - (16/2)²) = √(100 - 64) = √36 = 6.

If a chord of a circle is 16 units long and the radius is 10 units, what is the distance from the center of the circle to the chord?

If a chord of a circle is 16 units long and the radius is 10 units, what is the distance from the center of the circle to the chord?

Step 1: Identify the length of the chord, which is given as 16 units.
Step 2: Find half of the chord length. Half of 16 is 8 units.
Step 3: Identify the radius of the circle, which is given as 10 units.
Step 4: Use the formula to find the distance from the center of the circle to the chord: distance = √(radius² - (half of chord length)²).
Step 5: Substitute the values into the formula: distance = √(10² - 8²).
Step 6: Calculate 10², which is 100.
Step 7: Calculate 8², which is 64.
Step 8: Subtract 64 from 100: 100 - 64 = 36.
Step 9: Take the square root of 36: √36 = 6.
Step 10: The distance from the center of the circle to the chord is 6 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 the radius and half the chord length.