A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)

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Q: A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)

Solution: Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.

Steps: 9

Step 1: Understand that a chord is a straight line connecting two points on the circle.
Step 2: Identify that the distance from the center of the circle to the chord is given as 5 cm.
Step 3: Recognize that the chord is 12 cm long, so half of the chord is 6 cm (12 cm / 2 = 6 cm).
Step 4: Visualize a right triangle formed by the radius (r), the distance from the center to the chord (5 cm), and half the chord (6 cm).
Step 5: Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (r) is equal to the sum of the squares of the other two sides: r² = (5 cm)² + (6 cm)².
Step 6: Calculate (5 cm)² = 25 and (6 cm)² = 36.
Step 7: Add these two results: 25 + 36 = 61.
Step 8: Find the radius by taking the square root of 61: r = √61.
Step 9: Calculate the approximate value of √61, which is about 7.81 cm.