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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 = - Mathematics

MCQ

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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Q 3 | Page 110
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