5.2.4.40 Various Problems on the Plane

Condition: let \ (i \) - the center inscribed in the triangle \ (a b c \) circles, a \ (j \) - the center of the entered circle. Prove that the described circle crosses \ (i j \) in its middle. (This point, according to the tradition of the Rusanovsky lyceum, is indicated \ (w \), and the statement is part of the lemma about the triliary.)