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प्रश्न
In the figure, AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C = 20°, find angle AOD.
उत्तर
Join OB,
In ΔOBC,
BC = OD = OB ...(Radii of the same circle)
∴ ∠BOC = ∠BCO = 20°
And Ext. ∠ABO = ∠BCO + ∠BOC
`=>` Ext. ∠ABO = 20° + 20° = 40° ...(i)
In ΔOAB,
OA = OB ...(Radii of the same circle)
∴ ∠OAB = ∠OBA = 40° ...(From (i))
∠AOB = 180° – ∠OAB – ∠OBA
`=>` ∠AOB = 180° – 40° – 40° = 100°
Since DOC is a straight line
∴ ∠AOD + ∠AOB + ∠BOC = 180°
`=>` ∠AOD + 100° + 20° = 180°
`=>` ∠AOD = 180° – 120°
`=>` ∠AOD = 60°
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