From the vertex of the right angle C of the triangle ABC, the medians CD and the bisector CF

From the vertex of the right angle C of the triangle ABC, the medians CD and the bisector CF are drawn. Find the angle DCF if the angle ABC = 35 degrees.

In a right-angled triangle, the median drawn to the hypotenuse is equal to half of the hypotenuse, which means CD = AB / 2 = AD = DB. So the triangle DCB is isosceles, so the angle DCB = 35 degrees. Angle C is a straight line, and CF is a bisector, so the angle FCB = 45 degrees. Angle FCB = angle DCF + angle DCB, from here we get that angle DCF = 45-35 = 10 degrees.
Answer: DCF angle = 10 degrees.