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

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

Options:

Correct Answer: 8

Solution:

Using the formula d = √(r^2 - (c/2)^2), where r = 10 and c = 16, we get d = √(10^2 - 8^2) = √(100 - 64) = √36 = 6.

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

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

Step 1: Identify the radius of the circle (r) and the length of the chord (c). Here, r = 10 cm and c = 16 cm.
Step 2: Calculate half the length of the chord. This is c/2 = 16 cm / 2 = 8 cm.
Step 3: Use the formula d = √(r^2 - (c/2)^2) to find the distance from the center to the chord.
Step 4: Substitute the values into the formula: d = √(10^2 - 8^2).
Step 5: Calculate 10^2, which is 100, and 8^2, which is 64.
Step 6: Subtract 64 from 100: 100 - 64 = 36.
Step 7: Take the square root of 36: √36 = 6.
Step 8: The distance from the center of the circle to the chord is 6 cm.

Circle Geometry – Understanding the relationship between the radius, chord length, and 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.