To calculate the length of the radius of circle A, we need to use the fact that BC is tangent to circle A. Let O be the center of circle A, and let r be the length of the radius of circle A. Then we have:
BC ⊥ OA (since BC is tangent to circle A) BC = 3 AB = 5
We can use the Pythagorean theorem in triangle ABC to find the length of AC:
AC^2 = AB^2 - BC^2 AC^2 = 5^2 - 3^2 AC^2 = 16 AC = 4
Since OA is perpendicular to segment BC at point D, we can use the Pythagorean theorem in triangle AOD to solve for the radius r:
r^2 = OD^2 + AD^2 r^2 = (BC/2)^2 + AC^2 r^2 = (3/2)^2 + 4^2 r^2 = 2.25 + 16 r^2 = 18.25 r = sqrt(18.25) r ≈ 4.27
Therefore , the length of the radius of circle A is approximately 4.27 units.