What is the length of a chord that is 6 cm away from the center of a circle with

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Question: What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)

Options:

Correct Answer: 8 cm

Solution:

Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.

What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)

What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)

Step 1: Identify the radius of the circle, which is 10 cm.
Step 2: Identify the distance from the center of the circle to the chord, which is 6 cm.
Step 3: Use the Pythagorean theorem formula: (radius)² = (distance from center)² + (half chord)².
Step 4: Substitute the known values into the formula: 10² = 6² + (half chord)².
Step 5: Calculate 10², which is 100, and 6², which is 36. So, the equation becomes: 100 = 36 + (half chord)².
Step 6: Rearrange the equation to find (half chord)²: (half chord)² = 100 - 36.
Step 7: Calculate 100 - 36, which equals 64. So, (half chord)² = 64.
Step 8: Take the square root of 64 to find half the length of the chord: half chord = 8 cm.
Step 9: Since this is half the chord, multiply by 2 to find the full length of the chord: full chord = 8 cm * 2 = 16 cm.

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