The distance from the center C to the point on the circle B is the radius.
radius = length of BC = x
Triangle ABC is a right triangle. The right angle (aka 90 degree angle) is at angle B as shown by the square marker.
Because we have a right triangle, we can use the pythagorean theorem
(leg1)^2 + (leg2)^2 = (hypotenuse)^2
(AB)^2 + (BC)^2 = (AC)^2
(22)^2 + (x)^2 = (x+14)^2
484 + x^2 = x^2 + 28x + 196
484 + x^2-x^2 = x^2 + 28x + 196-x^2
484 = 28x+196
484-196 = 28x+196-196
288 = 28x
28x = 288
28x/28 = 288/28
x = 72/7
x = 10.285714
The exact value of x, as a fraction is 72/7
Using a calculator, the approximate value of x is roughly 10.285714
So the radius is exactly 72/7 units long.
The radius is approximately 10.285714 units long.