## 29. Triangle

How to construct a triangle, knowing its perimeter, one angle, and the height dropped from this angle?
29. Construct an angle with vertex $A$, equal to the given one. Let $D$ and $E$ be points on the sides of the angle, at a distance from $A$ equal to half the given perimeter,

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-168.jpg?height=911&width=966&top_left_y=1615&top_left_x=545)
and let $O$ be the point of intersection of the perpendiculars erected to the sides of the angle at points $D$ and $E$. Draw a circle with center $O$ and radius $O D=O E$. Then draw another circle with center $A$ and radius equal to the given height $h$. Finally, construct the common (internal) tangent to these two circles, intersecting the sides of angle $A$ at points $B$ and $C$. Then

$$
A B+B C+C A=A D+A E=\text { perimeter. }
$$

Thus, triangle $A B C$ is the desired triangle.