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


Hence, proved.

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