O is the circum-centre of the triangle ABC and OD ⊥ BC. Prove that ∠BOD = ∠BAC
Given: In ΔABC, O is the circumcentre and OD ⊥ BC.
Construction: Join BO and CO.
Proof: ΔBOD @ DDOC (R.H.S.) ∠BOD = ∠DOC =
∠BOC
Also ∠BOC = 2∠BAC
Þ 2∠BOD = 2∠BAC ⇒ ∠BOD = ∠BAC
Construction: Join BO and CO.
Proof: ΔBOD @ DDOC (R.H.S.) ∠BOD = ∠DOC =
∠BOCAlso ∠BOC = 2∠BAC
Þ 2∠BOD = 2∠BAC ⇒ ∠BOD = ∠BAC
19