The bisector of angle $A$ of triangle $ABC$ meet its circumcircle $\omega$ at point $W$. The circle $s$ with diameter $AH$ ($H$ is the orthocenter of $ABC$) meets $\omega$ for the second time at point $P$. Restore the triangle $ABC$ if the points $A$, $P$, $W$ are given.
1. **Identify the given points and circles:**
   - Points \( A \), \( P \), and \( W \) are given.
   - \( W \) is the point where the angle bisector of \(\angle A\) meets the circumcircle \(\omega\) of \(\triangle ABC\).
   - Circle \( s \) has diameter \( AH \), where \( H \) is the orthocenter of \(\triangle ABC\), and it intersects \(\omega\) at point \( P \).

2. **Determine the properties of the points and lines:**
   - Since \( W \) is on the angle bisector of \(\angle A\), it implies that \( W \) lies on the circumcircle \(\omega\).
   - The circle \( s \) with diameter \( AH \) implies that \( P \) is on both \(\omega\) and \( s \).
   - The line \( AP \) is perpendicular to \( PH \) because \( P \) lies on the circle with diameter \( AH \).

3. **Construct the circumcenter \( O \) of \(\triangle ABC\):**
   - The circumcenter \( O \) of \(\triangle ABC\) is the center of the circle passing through points \( A \), \( P \), and \( W \).

4. **Determine the midpoint \( M \) of \( BC \):**
   - The perpendicular to \( AP \) through \( P \) intersects the line \( OW \) at \( M \), which is the midpoint of \( BC \).

5. **Find the vertices \( B \) and \( C \):**
   - The points of intersection of the circle \((APW)\) with the perpendicular to \( OW \) through \( M \) are the vertices \( B \) and \( C \) of the triangle.

6. **Construct the triangle \( ABC \):**
   - Using the points \( A \), \( B \), and \( C \) determined in the previous steps, construct the triangle \( ABC \).

7. **Verify the construction:**
   - Ensure that the constructed triangle satisfies all given conditions, including the orthocenter \( H \) and the properties of the circumcircle and angle bisectors.

The final answer is the construction of triangle \( \boxed{ ABC } \) using the given points \( A \), \( P \), and \( W \).