Q. O IS THE CENTRE and AB is a chord. AC is the bisector of angle OAB .OAB = 56
a) prove that OC and AB are parallel
b) find angle ABC and OBE.

Dear Student,

Given : O is the centre and AB is a chord. AC is the bisector of OAB which is 56°.To Prove : OCAB   then To Calculate : ABC and OBE.Solution : Since AC is the angle bisector of OAB=56°OAC=CAB=562=28° Now, from arc BCBOC=2CAB (Angle subtended by an arc on centre is double the angle subtended on circumference)BOC=2×28°=56°Now,OA=OB (Radius of the circle)so, OAB is isosceles with OA=OBso,OAB=ABO=56°Now, since, ABO=BOC=56°Alternate interior angles are equal OCAB Now, in OBCOB=OC(Radius) OCB=OBCBOC+2OBC=180° 56°+2OBC=180° 2OBC=180° -56°2OBC=124°OBC=124°2OBC=62°Now, OBA+OBC+CBE=180° (angles on a straight line)56°+62°+CBE=180°CBE=180°-56°-62°CBE=62°Now, Required anglesABC=ABO+OBC=56°+62°=118°OBE=OBC+CBE=62°+62°=124°

Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Keep posting!!


  • 0
  • 1
correct <OBE = 124°
  • 0
  • 1
What are you looking for?