Question 96
Two circles $k_{1}$ and $k_{2}$ meet at points $A$ and $B$. A line through $B$ meets the circles $k_{1}$ and $k_{2}$ at points $X$ and $Y$, respectively. The tangent lines to $k_{1}$ at $X$ and to $k_{2}$ at $Y$ meet at $C$. Prove that:
a) $\measuredangle X A C = \measuredangle B A Y$.
b) $\measuredangle X B A = \measuredangle X B C$, if $B$ is the midpoint of $X Y$.
a) $\measuredangle X A C = \measuredangle B A Y$.
b) $\measuredangle X B A = \measuredangle X B C$, if $B$ is the midpoint of $X Y$.