Finding the Radius of a Circle from a Chord

In a circle, a chord measures 10 cm and is 6 cm away from the center of the circle. What is the radius of the circle?

To find the radius of the circle given a chord, we can use the relationship that if a perpendicular line is drawn from the center of the circle to the chord, it bisects the chord. Let's denote:

- $r$: the radius of the circle

- $d$: the distance from the center to the chord (6 cm)

- $c$: half the length of the chord (5 cm)

Using the Pythagorean theorem, we can establish the equation:

$$r^2 = d^2 + c^2$$