Question

$AB$ is a fixed diameter of a circle whose centre is $O$. From $C$, any point on the circle, a chord $CD$ is drawn perpendicular to $AB$. Then, as $C$ moves over a semicircle,the bisector of angle $OCD$ cuts the circle in a point that always:

• A. bisects the arc $AB$
• B. trisects the arc $AB$
• C. varies
• D. is as far from $AB$ as from $D$
• E. is equidistant from $B$ and $C$

Answer 1

Answer: (A)

bisects the arc $AB$

$\angle \theta$ cuts the circle in a point that always bisects are $AB$.