Which of the following triangles is congruent to which triangle:

In the figure, chord $BC$ is extended to $P$. Tangent from $P$ to the circle is $PA$. $AQ$ is the bisector of $\angle BAC$. Prove that $\angle PAQ=\frac{y+x}{2}$

In the figure, chord $BC$ is extended to $P$. Tangent from $P$ to the circle is $PA$. $AQ$ is the bisector of $\angle BAC$. If $\angle PAC=x$ and $\angle PCA=y$, then prove that $\angle BAC=y–x$.