Bakayev E.V.

On a line, four points are marked, and one more point is marked outside the line. In total, there are six triangles with vertices at these points.

What is the maximum number of them that can be isosceles?
Let's take an isosceles triangle with an angle of $108^{\circ}$. We will divide this angle into three equal parts (see figure). The six resulting triangles will be isosceles.

![](https://cdn.mathpix.com/cropped/2024_05_06_9fc5d17caeb61bf6ddabg-13.jpg?height=217&width=548&top_left_y=1795&top_left_x=755)

## Answer

All six.