## Task 3 - 040823

Given are the two adjacent angles $\alpha$ and $\beta$ with the vertex $A$ and point $D$ on the common side (see figure below).

a) Construct from this figure the triangle $A B C$ such that $\overline{A D}$ is a median!

b) Under what condition will the triangle $A B C$ be equilateral?

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0596.jpg?height=220&width=371&top_left_y=1112&top_left_x=1365)