AB is a chord of a circle whose centre is O. if P is any point on the minor arc AB prove that angleAOB+ 2angleAPB=360

Dear Student,

Please find below the solution to the asked query:

We form our diagram from given information , As :

Here , AB is a given chord .

We know : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle .

So,

Reflex $\angle$ AOB  = 2 $\angle$ APB                            ---- ( 1 )

And

Reflex $\angle$ AOB  +  $\angle$ AOB  =  360$°$            ( Angle around the center of circle ) 

Substitute value from equation 1 and get

 $\angle$ AOB  + 2 $\angle$ APB   =  360$°$                    ( Hence proved )


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