Question

In the figure shown, $O$ is the centre of the circle. Chord $CD$ is parallel to the diameter $AB$. If $\angle ABC={35}^o$, Calculate $\angle CED$.

Answer 1

Given $\angle ABC={35}^o$

Now, $\angle AOC$ subtended by the chord AC at the centre O of circle will be double the $\angle ABC$ subtended by same chord AC at point B on corresponding segment of circle thus

$\angle AOC=2\angle ABC=2\times {35}^o={70}^o$

$\angle BOD=\angle AOC={70}^o$

But

$\angle AOC+\angle COD+\angle BOD={180}^o$

${70}^o+\angle COD+{70}^o={180}^o$

$\angle COD={40}^o$

Now, $\angle COD$ subtended by the chord CD at the centre O of circle will be double the $\angle CED$ subtended by same chord CD at point E on corresponding segment of circle thus

$\angle COD=2\angle CED$

${40}^o=2\angle CED$

$\angle CED={20}^o$