Question 1
Given two circles $(O_1), (O_2)$ with different radii and intersecting at two points $A, B$. The tangent $CD$ of the two circles (closer to point $B$) with $C \in (O_1)$ and $D \in (O_2)$. Draw diameters $BP, BQ$ of $(O_1), (O_2)$. The line through $B$, and perpendicular to $CD$ cuts $PQ$ at $K$.
a) Prove that $B$ is the orthocenter of triangle $KCD$.
b) Draw the angle bisectors $BX, BY$ of the triangles $KBP, KBQ$ respectively with $X, Y \in PQ$. Prove that $KX = KY$.
a) Prove that $B$ is the orthocenter of triangle $KCD$.
b) Draw the angle bisectors $BX, BY$ of the triangles $KBP, KBQ$ respectively with $X, Y \in PQ$. Prove that $KX = KY$.