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Question -

O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A



Answer -

We have to prove that  

Since, circumcenter is the intersection of perpendicular bisectors of each side of the triangle.
Now according to figure A, B, C are the vertices of ΔABC
In  ,   is perpendicular bisector of BC
So, BD = CD                 
OB = OC             (Radius of the same circle)
And,
OD = OD         (Common)
We know that angle formed any chord of the circle at the center is twice of the angle formed at the circumference by same chord
Therefore,
 
Therefore,
 
Hence proved

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