Question

Prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc.

Answer 1

Let XY be the tangent at the mid point of the arc A

Let TT be the point of contact



Let ABAB 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.

ABAB is parallel to xy