Problem 489

8.7. Suppose that triangle $A B C$ is constructed. Let $A_{1}$ and $C_{1}$ be the midpoints of sides $C B$ and $A B$. Since $C_{1} A_{1} \| A C$, then $\angle A_{1} C_{1} B=\angle A$. From this, the following construction follows. First, construct segment $C B$ of length $a$ and its midpoint $A_{1}$. Point $C_{1}$ is the intersection of the circle of radius $m_{c}$ centered at $C$ and the arcs of circles from which segment $A_{1} B$ is seen at angle $A$. By constructing point $C_{1}$, lay off segment $B A=2 B C_{1}$ on ray $B C_{1}$. Then $A$ is the desired vertex of the triangle.