Geometry · Incenter · Angle bisectors · Cyclic quadrilaterals · Inscribed angle theorem · Isosceles triangles · Area
In triangle \(ABC\) the bisector of the angle \(CAB\) meets the side \(BC\) at the point \(N\), and the bisector of the angle \(CBA\) meets the side \(AC\) at the point \(P\), where
Let \(Q\) be the intersection of the two bisectors \(AN\) and \(BP\). The vertex \(C\) lies on the circle through the points \(P\), \(Q\) and \(N\). Find the area of triangle \(NPQ\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 1997, high school grade I, problem 3. The 1997 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).