Finding the radius of a circle when you have the length of a chord and the distance from the chord to the center of the circle involves a bit of geometry and algebra. Here’s a step-by-step process to guide you:

Steps to Calculate the Radius:

1. Understand the Components:
   Identify the chord length (let’s call it c) and the perpendicular distance from the midpoint of the chord to the center of the circle (let’s call it d).
2. Divide the Chord:
   Since the midpoint of the chord creates two equal segments, divide c by 2 to get half the length of the chord (c/2).
3. Use the Pythagorean Theorem:
   In the right triangle formed by the radius, half the chord, and the distance d, apply the Pythagorean theorem. The relationship can be expressed as:

   r2 = (c/2)2 + d2

   Where r is the radius of the circle.

4. Solve for the Radius:
   Rearranging the formula will give you:

   r = √((c/2)2 + d2)

   Plug in your known values for c and d and calculate the radius.

Example:

Suppose you have a chord that is 10 units long, and the distance from the chord to the circle’s center is 4 units:

1. c = 10, therefore c/2 = 5
2. d = 4
3. Apply the Pythagorean theorem:
   r = √(52 + 42)
   r = √(25 + 16) = √41 ≈ 6.4

The radius of the circle is approximately 6.4 units.

This method is efficient and allows for a clear calculation of the radius using only the chord length and its distance to the center. Remember to ensure accurate measurements to achieve the correct radius.