Question

AB and BC are two equal chords of a circle with center O. If angle BOC=80 degree then angle AOB is?​

Answer 1

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∠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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