5.2.4.35 Various Problems on the Plane

Condition: Two circles apply external at point \ (k \). Direct \ (a b \) applies to the first circle at the point \ (a \), and the second at the point \ (b \). Direct \ (b k \) crosses the first circle at the point \ (d \), straight \ (a k \) crosses the second circle at point \ (C \). a) Prove that the triangle \ (a k b \) and \ (d k c \) have equal areas. b) Find the area of the triangle \ (a k b \) if it is known that the radii of circles are 4 and 1.