5.2.4.35 Various problems on the plane

Condition: Two circles touch externally at the point \(K\). The straight line \( A B \) touches the first circle at the point \( A \), and the second - at the point \( B \). The straight line \(B K\) intersects the first circle at the point \(D\), the straight line \(A K\) intersects the second circle at the 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 the circles are 4 and 1.