A chord of a circle is 10 cm long and is 6 cm away from the center. What is the

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Question: A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)

Options:

Correct Answer: 10 cm

Exam Year: 2023

Solution:

Using Pythagoras theorem: r² = (10/2)² + 6²; r² = 25 + 36 = 61; r = √61 ≈ 10 cm.

A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)

A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)

Step 1: Identify the length of the chord, which is 10 cm.
Step 2: Find the distance from the center of the circle to the chord, which is 6 cm.
Step 3: Calculate half the length of the chord. Since the chord is 10 cm long, half of it is 10/2 = 5 cm.
Step 4: Use the Pythagorean theorem. In a right triangle formed by the radius (r), half the chord (5 cm), and the distance from the center to the chord (6 cm), we have: r² = (half the chord)² + (distance from center to chord)².
Step 5: Substitute the values into the equation: r² = 5² + 6².
Step 6: Calculate 5², which is 25, and 6², which is 36.
Step 7: Add these two results together: 25 + 36 = 61.
Step 8: To find the radius, take the square root of 61: r = √61.
Step 9: Calculate the approximate value of √61, which is about 10 cm.

Pythagorean Theorem – The relationship between the lengths of the sides of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Circle Geometry – Understanding the properties of circles, including the relationship between chords, radii, and distances from the center.