Q. 134.6( 8 Votes )

O is the circumcentre of Δ ABC and OD is perpendicular on the side BC; let us prove that BOD = BAC

Answer :


By the theorem:-


The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.


BOC = 2 BAC ------------ (1)


In ΔBOD and COD,


BDO = CDO = 90° (given)


OD = OD (common)


OB = OC (radius)


Therefore, ΔBOD COD by RHS congruency


BOD = COD ------------------- (2)


From (1) and (2), we get,


2 BOD = 2 BAC


BOD = BAC


Hence, proved.


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