If a chord of a circle is 10 cm long and the radius is 6 cm, what is the distanc

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Question: If a chord of a circle is 10 cm long and the radius is 6 cm, what is the distance from the center of the circle to the chord?

Options:

Correct Answer: 3 cm

Solution:

Using the Pythagorean theorem, the distance from the center to the chord is √(r² - (c/2)²) = √(6² - 5²) = √(36 - 25) = √11 cm.

If a chord of a circle is 10 cm long and the radius is 6 cm, what is the distance from the center of the circle to the chord?

If a chord of a circle is 10 cm long and the radius is 6 cm, what is the distance from the center of the circle to the chord?

Step 1: Identify the given values. The length of the chord (c) is 10 cm and the radius (r) of the circle is 6 cm.
Step 2: Find half the length of the chord. Since the chord is 10 cm long, half of it is 10 cm / 2 = 5 cm.
Step 3: Use the Pythagorean theorem to find the distance (d) from the center of the circle to the chord. The formula is d = √(r² - (c/2)²).
Step 4: Substitute the values into the formula. Here, r = 6 cm and c/2 = 5 cm, so we have d = √(6² - 5²).
Step 5: Calculate r² and (c/2)². r² = 6² = 36 and (c/2)² = 5² = 25.
Step 6: Subtract (c/2)² from r². So, 36 - 25 = 11.
Step 7: Take the square root of the result. d = √11 cm.
Step 8: Conclude that the distance from the center of the circle to the chord is √11 cm.

Pythagorean Theorem – The relationship between the lengths of the sides of a right triangle, used to find the distance from the center of the circle to the chord.
Circle Geometry – Understanding properties of circles, including chords, radii, and distances from the center.