Question 69
A circle with diameter $AB$ and centre $O$ is given. Let $C$ be a point on the circle (different from $A$ and $B$), and draw the line $r$ through $O$ parallel to $AC$. Let $D$ be the intersection of $r$ with the circle, on the opposite side of $C$ with respect to $AB$.
i) Prove that $DO$ is the bisector of $\angle CDB$.
ii) Prove that the triangle $CDB$ is similar to the triangle $AOD$.
i) Prove that $DO$ is the bisector of $\angle CDB$.
ii) Prove that the triangle $CDB$ is similar to the triangle $AOD$.