A chord of a circle is 8 cm long and is 3 cm away from the center. What is the r

A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)

A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)

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 3 cm.
Step 3: Recognize that the chord is 8 cm long, so half of the chord is 4 cm (8 cm / 2 = 4 cm).
Step 4: Visualize a right triangle formed by the radius (r), the distance from the center to the chord (3 cm), and half the chord (4 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 = (3 cm)² + (4 cm)².
Step 6: Calculate (3 cm)² = 9 and (4 cm)² = 16.
Step 7: Add these two results: 9 + 16 = 25.
Step 8: Take the square root of 25 to find the radius: r = √25 = 5 cm.

Circle Geometry – Understanding the relationship between the radius, chord length, and distance from the center of the circle.
Pythagorean Theorem – Applying the theorem to find the radius using the right triangle formed by the radius, half the chord, and the distance from the center.