Question

in the figure O is the centre of the circle and OABC is a parallelogram. Find angle ABC and angle OAB​

Answer 1

Solution :-

Construction :- Join OB .

Now,

→ OA = OB = OC { Radius of circle. }

and,

→ AB = OC and OA = BC { Opposite sides of || gm are equal. }

So, In ∆OAB,

→ OA = OB = AB

and,

In ∆OCB,

→ OC = OB = BC

therefore, we can conclude that,

• ∆OAB and ∆OCB are equilateral ∆'s .
• All angles of an equaliteral ∆ is equal to 60° .

hence,

→ ∠ABC = ∠OBA + ∠OBC

→ ∠ABC = 60° + 60°

→ ∠ABC = 120° (Ans.)

and,

→ ∠OAB = 60° (Ans.)

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