In the given figure, O is the centre of a circle in which ∠OAB = 20° and

Question:

In the given figure, O is the centre of a circle in which OAB = 20° and ∠OCB = 55°. Find ]\

(i) ∠BOC,

(ii) ∠AOC

 

Solution:

(i)
OB = OC (Radii of a circle)
⇒ OBC = OCB = 55°
Considering ΔBOC, we have:
BOC + OCB + OBC = 180° (Angle sum property of a triangle)
BOC + 55° + 55° = 180°
BOC = (180° - 110°) = 70°

(ii)
OA = OB          (Radii of a circle)
⇒ OBA = OAB = 20°
Considering ΔAOB, we have:
AOB + OAB + OBA = 180°    (Angle sum property of a triangle)
AOB + 20° + 20° = 180°
AOB = (180° - 40°) = 140°
∴ AOC = AOB - BOC

= (140° - 70°)  

= 70°

Hence, ∠AOC = 70°

 

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