in the given figure, 'O' is the centre of the circle and the length of arc AB is twice
the length of arc BC. If LAOB = 104", find by giving reasons:
(0) LBOC
(1) LOAC
() ZBAC
Answers
∠BOC = 52° , ∠OAC = 12° , ∠BAC = 26°
Step-by-step explanation:
∠AOB = 104°
Arc length AB = (∠AOB/360°) * 2 π * Radius
Arc length BC = (∠BOC/360°) * 2 π * Radius
length of arc AB is twice the length of arc BC
=> (∠AOB/360°) * 2 π * Radius = 2 * (∠BOC/360°) * 2 π * Radius
=> ∠BOC = ∠AOB/2
=> ∠BOC = 104°/2
=> ∠BOC = 52°
∠BAC = (1/2)∠BOC ( angle subtended by chord BC at center & arc segment)
=> ∠BAC = 52°/2 = 26°
in Δ OAB
OA = OB = Radius
=> ∠OAB = ∠OBA
∠AOB = 104°
∠OAB + ∠OBA + ∠AOB = 180°
=> ∠OAB = ∠OBA = 38°
∠OAC = ∠OAB - ∠BAC
=> ∠OAC = 38° - 26°
=> ∠OAC = 12°
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Answer:
the answer is angle oac is 12 degree