Inscribe a rhombus in a triangle

Let the other vertices of the triangle be $B$ and $C$ .

1. Draw a circle centred at $A$ of arbitrary radius such that it intersects $AB$ and $AC$ at $P$ and $Q$ . (1 move)

2. Draw circles centred at $P$ and $Q$ passing through $A$ . Let these circles intersect each other again at $R$ . (3 moves)

3. Draw $AR$ let it intersect $BC$ at $E$ . (4 moves)

4. Draw a circle centred at $A$ passing through $E$ . Draw a circle centred at $E$ passing through $A$ . Let these two circles intersect each other at $M$ and $N$ . (6 moves)

5. Draw $MN$ . Let this line intersect $AB$ and $AC$ at $D$ and $F$ .

6. Draw $DE$ and $EF$ .

Here, $ADEF$ is a rhombus, sharing an angle with triangle $ABC$ , and it took 9 moves.