Let $I$ be the center of the inscribed circle of the triangle $ABC$. The inscribed circle is tangent to sides $BC$ and $AC$ at points $K_1$ and $K_2$ respectively. Using a ruler and a compass, find the center of excircle for triangle $CK_1K_2$ which is tangent to side $CK_2$, in at most $4$ steps (each step is to draw a circle or a line).

(Hryhorii Filippovskyi, Volodymyr Brayman)
1. **Draw the line \( K_1K_2 \)**:
   - Using a ruler, draw the line segment \( K_1K_2 \) which is tangent to the inscribed circle at points \( K_1 \) and \( K_2 \).

2. **Construct a line \( L \) through \( C \) parallel to \( K_1K_2 \)**:
   - Use the angle-copy method to construct a line \( L \) through point \( C \) that is parallel to \( K_1K_2 \). This involves:
     - Drawing a transversal line through \( C \) intersecting \( K_1K_2 \).
     - Copying the angle formed between the transversal and \( K_1K_2 \) to the other side of the transversal at \( C \).
     - Drawing the parallel line \( L \) through \( C \).

3. **Draw a circle \( P \) centered at \( C \) with radius \( CK_1 \)**:
   - Using a compass, set the radius to the length of \( CK_1 \).
   - Draw the circle \( P \) centered at \( C \) with this radius.

4. **Find the intersection of line \( L \) and circle \( P \)**:
   - The intersection point \( D \) of the line \( L \) and the circle \( P \) is the excenter of the triangle \( CK_1K_2 \) that is tangent to side \( CK_2 \).

To summarize, the steps are:
1. Draw \( K_1K_2 \).
2. Construct a parallel line \( L \) through \( C \).
3. Draw a circle \( P \) centered at \( C \) with radius \( CK_1 \).
4. Find the intersection of \( L \) and \( P \) to locate the excenter \( D \).

The final answer is the intersection point \( \boxed{ D } \) of the line \( L \) and the circle \( P \).