o is the centre of the circle and ab is a chord{ao and bo is joined} ab is produce to - Maths - Circles

Question

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

Anuradha Sharma · Accepted Answer

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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 = 180∠AOB = 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