If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm awa

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Question: If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center of the circle?

Options:

Correct Answer: 6 cm

Solution:

Using the Pythagorean theorem, the length of the chord can be calculated as 2 * sqrt(5^2 - 4^2) = 6 cm.

If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center of the circle?

If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center of the circle?

Step 1: Understand that a chord is a straight line connecting two points on the circle.
Step 2: Identify the radius of the circle, which is given as 5 cm.
Step 3: Recognize that the distance from the center of the circle to the chord is 4 cm.
Step 4: Visualize a right triangle formed by the radius, the distance from the center to the chord, and half the length of the chord.
Step 5: Label the radius as 'r' (5 cm), the distance from the center to the chord as 'd' (4 cm), and half the length of the chord as 'x'.
Step 6: Use the Pythagorean theorem, which states that r^2 = d^2 + x^2.
Step 7: Substitute the known values into the equation: 5^2 = 4^2 + x^2.
Step 8: Calculate 5^2, which is 25, and 4^2, which is 16: 25 = 16 + x^2.
Step 9: Rearrange the equation to find x^2: x^2 = 25 - 16.
Step 10: Calculate 25 - 16, which equals 9: x^2 = 9.
Step 11: Take the square root of 9 to find x: x = 3 cm.
Step 12: Since x is half the length of the chord, multiply by 2 to find the full length of the chord: Length of chord = 2 * 3 = 6 cm.

Circle Geometry – Understanding the properties of circles, including chords, radii, and distances from the center.
Pythagorean Theorem – Applying the Pythagorean theorem to find the length of a chord based on its distance from the center.