(a) A triangle ABC has sides AB = 4, AC = 3, BC = 5. A semicircle is drawn so that its diameter lies on AB and one end of the diameter is at A. What is the largest possible radius of the semicircle if it fits inside the triangle?

(b) In the same triangle ABC, a semicircle is instead drawn so that its diameter lies on BC. What is the largest possible radius of the semicircle if it fits inside the triangle?