o is the centre of the circle and ab is a chord{ao and bo is joined} ab is produce to c and oc is joined and oc is extended to d{abc and doc is a straight line}
in the given figure ,ab is a chord of a circle with centre o . abiss produced to c such that bc=ob,also.co is joined and produced to meet the circle at d .if angleacd=y and angle aod=x, prove that x=3y.if angle aod=60,find angle aob

Here BO = BC so BCO=BOC=yNow angle ABO is the external angle to triangle OBC so, ABO= y+y=2y Now OA= OB= radius SO OAB=OBA=2y Now in triangle OAB, 2y+2y+AOB= 180AOB= 180-4yNow using linear pair, x+180-4y+y = 180x = 3y Given x = 60 degreeSo y = 20 degreeSo Angle AOB= 180-4×20=100 degree

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