# Q: 1     In Fig.  $\small 10.36$, A,B and C are three points on a circle with centre  O such that $\small \angle BOC=30^{\circ}$  and  $\small \angle AOB=60^{\circ}$. If D is a point on the circle other than the arc ABC, find $\small \angle ADC$.

$\angle$AOC = $\angle$AOB + $\angle$BOC= $60 \degree+30 \degree=90 \degree$

$\angle$AOC = 2 $\angle$ADC   (angle subtended by an arc at the centre is double the angle subtended by it at any)

$\angle ADC=\frac{1}{2}\angle AOC$

$\Rightarrow \angle ADC=\frac{1}{2}90 \degree= 45 \degree$

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