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  • In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

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.

            

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\angleAOC = \angleAOB + \angleBOC= 60 \degree+30 \degree=90 \degree

\angleAOC = 2 \angleADC   (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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