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In figure below, $A,B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC = 30^o$ and $\angle AOB = 60^o$. If $D$ is a point on the circle other than the arc $ABC$, find $\angle ADC$.
"
Given:
$A,B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC = 30^o$ and $\angle AOB = 60^o$.
$D$ is a point on the circle other than the arc $ABC$.
To do:
We have to find $\angle ADC$.
Solution:
$\angle AOC = \angle AOB+\angle BOC$
$\angle AOC = 60^o+30^o$
$\angle AOC = 90^o$
We know that,
The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the circle.
Therefore,
$\angle ADC = \frac{1}{2}\angle AOC$
$= \frac{1}{2}\times 90^o$
$= 45^o$
Hence, $\angle ADC =45^o$.
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