Question

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

Answer 1

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 .