Q19 of 62 Page 10

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

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