Question

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

Answer 1

In ΔOBD and ΔOCD: 

OB = OC [Radius] 

∠ODB = ∠ODC [Each 90°] 

OD = OD [Common] 

Therefore, By RHS Condition 

ΔOBD ≅ ΔOCD 

So, ∠BOD = ∠COD…..(i)[By CPCT] 

Again, By degree measure theorem: 

∠BOC = 2∠BAC 

2∠BOD = 2∠BAC [Using(i)] 

∠BOD = ∠BAC 

Hence proved.