prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining at the end points of the arc
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Let XY be the tangent at the mid point of the arc A
Let
T
T
be the point of contact
Let
AB
AB
be the chord
Since T is the mid point , Distance mid point of AB.
Construction join OA ,OB and OT , where O is the centre of the circle .
Proof :
∠OTY=
90
∘
∠OTY=90∘
∠ODB=
90
∘
∠ODB=90∘
Since the alternate interior angles are equal.
AB
AB
is parallel to xy
Hence proved .
Let
T
T
be the point of contact
Let
AB
AB
be the chord
Since T is the mid point , Distance mid point of AB.
Construction join OA ,OB and OT , where O is the centre of the circle .
Proof :
∠OTY=
90
∘
∠OTY=90∘
∠ODB=
90
∘
∠ODB=90∘
Since the alternate interior angles are equal.
AB
AB
is parallel to xy
Hence proved .
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