8,9

In an isosceles triangle \(ABC (AB = BC)\), the medians \(AM\) and \(CN\) intersect at point \(D\) at a right angle. Find all the angles of triangle \(ABC\) and its base \(AC\), if the area of quadrilateral \(NBMD\) is 4.
The medians of a triangle intersect at one point and are divided by it in the ratio 2:1, counting from the vertex.

## Answer

$\angle A=\angle C=\operatorname{arctg} 3 ; \angle B=\pi-2 \operatorname{arctg} 3 ; 4$.