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Question
If O is the centre of a circle of radius r and AB is a chord of the circle at a distance r/2 from O, then ∠BAO =
Options
60°
45°
30°
15°
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Solution
We will associate the given information in the following figure.
Since AO = r (radius of circle)
AM = `r/2` (given)
Extended OM to D where MD = `r/2`
Consider the triangles AOM and triangle AMD
OM = MD
`angleAMO = angle AMD` = 90°
AM = AM (common Sides
So by SSS property
Δ AMO ≅ Δ DM
So AD = AO = r and OD=OM+MD=r
Hence ΔAOD is equilateral triangle
So `angle OAD` = 60°
We know that in equilateral triangle altitudes divide the vertex angles
Therefore `angleOAM = (angleOAD)/2`
`=60/2`
= 30°
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