If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm fr

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Question: If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)

Options:

Correct Answer: 5 cm

Exam Year: 2014

Solution:

Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.

If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)

If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)

Step 1: Identify the radius of the circle, which is given as 4 cm.
Step 2: Identify the distance from the center of the circle to the chord, which is given as 3 cm.
Step 3: Use the Pythagorean theorem to find the length of the chord. The formula is: chord length = 2√(r² - d²), where r is the radius and d is the distance from the center to the chord.
Step 4: Substitute the values into the formula: chord length = 2√(4² - 3²).
Step 5: Calculate 4², which is 16, and 3², which is 9.
Step 6: Subtract 9 from 16 to get 7: 16 - 9 = 7.
Step 7: Take the square root of 7: √7.
Step 8: Multiply the result by 2 to find the chord length: 2√7.
Step 9: Calculate the approximate value of 2√7, which is about 5.29 cm.

Circle Geometry – Understanding the properties of circles, including the relationship between the radius, distance from the center, and chord length.
Pythagorean Theorem – Applying the Pythagorean theorem to find the length of a chord based on the radius and distance from the center.