Question

If $\angle OAB=40°$ and $AB=CD$, then find the measure of $\angle COD$.

Answer 1

Construction: Draw lines $OB$, $OC$, and $OD$.
In $\Delta AOB$,
$OA=OB$ (Radii of the same circle)
Thus, $\angle OAB=\angle OBA=40°$.
(Angles opposite to equal sides of a triangle).
So, by angle sum property, $\angle AOB=100°$.
Since the chords $AB$ and $CD$ are equal in length, the angles subtended by them at the centre will be equal.
Hence, $\angle AOB=\angle COD=100°$.