Question

prove that the tangents drawn at the mid-point of an arc of a circle is parallel to the base to the cord joining the end points of the arc

Answer 1

Let XY be the tangent at the mid point of the arc A Let T be the point of contact Let 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.

ABAB is parallel to xy

Hence proved .

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