Geometry · Incircle · Tangent lengths · Midline · Angle bisector · Concurrency
Let \(ABC\) be a triangle. Prove that the following three lines all pass through one point:
the bisector of the angle at \(A\); the line through the midpoints of the sides \(CA\) and \(CB\); and the line through the two points at which the incircle of the triangle touches the sides \(AB\) and \(BC\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2017, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source